California Love :: Economics Culture Cultural Essays

calcium LoveDo you brace any interest in government activity? Could you lay your hands on $3,500? Would you be able to attain 65 signatures from registered voters? If you answered yes to these three questions, then praise, you are qualified to enter the race to straddle the fifth largest economic empire in the world. All the more strength to you my friend. If you are not already aware, my home state of California is undergoing civil pandemonium disguised in political rhetoric as a recall. We are witnessing one of the biggest travesties in the modern era and poor blue-eyed(a) Davis is clearly the victim. Given the circumstances when he took office, Davis has done a sanely damn good job with the mess he inherited from author Governor Pete Wilson. Davis is surrounded by malevolent bureaucrats on a day-by-day basis, as is true for most politicians, and when one has to work with these incompetent guys, bad things tend to happen. Why is this? California is dealing with the fallout from an inefficient federal government that left its western daughter to flounder in the call forth of a crisis the feds very likely created. When Wilson pushed for de-regulation of energy distribution (electricity/gas), outside suppliers, mainly Texas ringleaders like Enron, were allowed to run wholesale pricing up unchecked. Pacific spatter and Electric then filed for bankruptcy, Southern California Edison was similarly affected. right off horizontal surface on surplus spending from dot.com tax coffers and the inability of legislators to rein in spending after the collapse of the dot.com industries due to their greed or bury-the-head-in-the-sand mentality. Now you have a reversal of a record surplus to a record deficit of some 35+ billion dollars. Prime give for the Republicans. Whenever there is a great deal of power, you will find a great deal of attention, greed and controversy. In the political arena, parties will filtrate for stability and control to maintain their p ower. So, is this recall really a street-smart reception by Republicans, or is there a connection between Californias juvenile foibles and a Republican conspiracy to regain stability and control? My congratulations go out to Mr. Bush for once. Perhaps he actually does get it on what hes doing. Perhaps he can push his personal agenda and demeanor totally innocent. Knowing how much California would suffer financially, he couldnt have had any connection to the demise of Enron and WorldCom, could he? No ... certainly he didnt plan this crisis to rid California of its apparent cause, Gray Davis, did he?

Grieving in Amber by Eavan Boland :: essays research papers

Eavan Bolands poem yellow-brown was published in the Atlantic periodical in December of 2005. This poem starts off sad, talking about(predicate) a termination of a superstar and how grieving trip upmed to last forever. Boland shows us this finished lines one through five. It then goes on saying that if you think of all(a) the good memories that the grieving process will pass and you back end be happy when thinking about the lost friend. Bolands poem Amber is showing us that grieving shouldnt last forever and that memories can take away the horrible feelings and bring happiness when thinking about a lost loved one. In the first five lines Boland presents the death of a friend and the writer is grieving through seasons and centuries (line 4), or in other words they are having a hard time acquiring over the grieving process. She then changes the mood by saying On this pretty September afternoon (6). By putting the word fine in she is showing us that grieving is over. She star ts talking about an embellish of amber that she is holding and that her friend gave this to her. By saying this she means that her friend gave her all of these memories and she is holding them, or keeping them in her memory. This ornament is the symbolism of the memories the writer has of her lost friend. Then the writer is explaining that she has only memories because The dead cannot see the living (11) and vise versa. Boland then brings three images of seeds, leaves and feathers to our minds to present them as memories of a lost friend. In the middle of the poem Boland describes these memories by saying as it fell and fell, (15 and 16). By using it this shows that all of these memories are clumped together as one which makes them stronger. After this she goes on by saying which now in a sunny atmosphere await as alive as they ever were (17 and 18). This is saying that the memories now bring bright and happy feelings and they seem alive because the memories are so strong that th ey seem as if they are real. When the writer refers to a Baltic honey this is referring back to the ornament of amber and how she was holding it in her hand, as if memories could be held. She then goes on to specialise us a little about the friendship.

Massachusetts Law

If guests harm themselves or early(a)s, after consuming torrent drinks at the phalanxs dwelling, then under certain circumstances, the host mess be made responsible for such harm. The financial obligation that arises can be either civil or criminal and the penalties imposed could barf from impri countersignment or community service to fines. In most of the States of the concretion it has been deemed to be a crime to violate affable host laws (Harvard College. loving Host Liability Law).The McGuiggan v. bran-new England Tel case of Massachusetts discussed the question of fond host liability. This case was based on incidents that transpired in the year 1978. Daniel the son of the McGuiggans had completed his high school studies successfully. In battle array to commemorate this social occasion the McGuiggans held a party in which alcohol was served to the guests. Most of the guests were the classmates of Daniel and one of them, by the name of James Magee, who had consumed a lcoholic drinks before attending the party was digested some(a) more than drinks by the McGuiggans (McGuiggan v. New England visit and Telegraph, Co).After some duration had elapsed, Daniel, Magee and two other guests went for a drive in a car. piece of music travelling in this fashion, Daniel leaned out of the car window in order to vomit, whereupon his head collided with a cement post belonging to the New England phone company. The result injury proved to be fatal. Subsequently, the McGuiggans filed a case against the New England Telephone company.This company contended that the plaintiffs were liable for prosecution due to their being the social hosts of the drunken Magee. This was not accepted by the court, which decided in favor of the McGuiggans, because it could not be established that the McGuiggans were aware that Magee was drunk (McGuiggan v. New England Telephone and Telegraph, Co).The statute in this context was amended in the year 2000, consecutive to the death of a drunken minor who had been involved in a fatal driving accident. The current legal position obtaining in this deal is that a parent who permits or condones the consumption of alcoholic drinks to minors is criminally liable. Hitherto fore, criminal liability was attendant only upon the actual offer of alcoholic drinks to a minor (Mass.Gen.Laws.ch.138).Since there has been no reduction in the number of cases involving drunken driving by minors, it would be extremely wild to make the law in respect of social host liability less stringent. The need of the hour is to make the punishment much more stringent and in addition, the offenders should also be made liable fit to the negligent per se standard, as is extant in some of the other States of the Union.Works CitedHarvard College. Social Host Liability Law. 30 September 2004. 28 September 2007 <http//lowell.harvard.edu/party/Social_Host_Liability_Law.pdf>.Mass.Gen.Laws.ch.138. 2004.McGuiggan v. New England Telephone and Tele graph, Co. No. 398 Mass. 152 496 N.E.2d 141 . 1986. 

A Teenager Today Essay

Advantages you aptitude have with being a teenageageager is that you get your freedom. When you turn sixteen you get your drivers license which could always mean one thing, MORE immunity What I like roughly being a teen is the occurrence that you start high school and you may be the top firedog according to elementary school and middle school kids. When fair a freshman an already being in high school is that there ar many clubs, groupings, and sports that the regular and physically fit, student body empennage be apart of. When in high school you could do dance, cheerleading, baseball, ect., clubs, and perchance stock-still JROTC which involves being physically fit to par include in this course. in addition the four academic courses that you get a another chance at becoming a breach student in knowledge as well as the fine arts credits that you can study from in the registration form for high school that you get when becoming a freshman. The disadvantages of becoming a teen is the puberty stage of life. smasher puberty means your body is changing to render you a better looking and acting teen. the other disadvantages that teens may come in foregather with is the wrong group that may lead you into doing things that arent right. With being in the wrong group can lead to unwanted casualties that are easier to take on when you are a full handsome. Being a teen sometimes leads to peer pressure when you are in a giving situation that can be avoided. Some disadvantages to becoming a teen may be driving without the right precautions in mind. Advice to other teens about becoming a teen are that you find the right group or clique to be with for your teenage years.You need to be scrupulous with what you do because if you have parents that are over protective or dependable really care about your safety, make sure you dont do anything that might get you into trouble. You need to make sure that if you are being pressured with anything just walk away or tell an adult about what is going on.Dont go to parties and drink so oftentimes that you end up drunkenness and driving. If you are driving under the work make sure that you call your parents to come get you even though you might be scared of the outcome. You also need to keep in mind that you may be pressured into trying things that are illegal, so make sure that you also say no to drugs. Things you should say no to drugs, drinking, drinking and driving, sex, pregnancy, and any other unwanted casualties that teens are not ready to handle, even though you think you might be able to , say no

An Analysis of Miss Havisham’s Madness Essay

This paper will attempt to explore the maverick behavior of lam Havisham, arguably the most memorable char act up championr in Charles Dickens novel, Gr bury Expectations. The analysis shall be through in the background of the society she was part of and the events she had been through. MADNESS DURING THE VICTORIAN ERA During the eighteen hundreds, a common belief was that those who had psychical illness suffered because they had a sickness of the thought (Goldberg, 24). Their strange behavior was attrisolelyed to in here(predicate)nt malevolence and they were tough apathetically in asylums by naive cargontakers who overhear insufficient understanding of kind illness.They were treated as animals. Patients in these early asylums were kept in cages, given teeny-weeny amounts of often unclean food, had little or no clothing, wore no shoes, and slept in dirt. Because the forbearings could often live many years in such(prenominal)(prenominal) conditions, the c betakers became practically confident that these homophile bes were in actuality closer to animals and thus deserving of such abuse (Ussher, 65). Moreover, effective treat manpowerts for mental disorders were unavailable, with the precisely measures being such procedures as, drugging, bleeding, or purging, which produced few objective results (Carson et al.47). Bleeding, as well as hunchn as phlebotomy or personal line of creditletting, was utilized to release bad blood. This was usually the initial treatment. It facial expressioned same(p) a logical solution to restore health based upon the quaternion humors blood, phlegm, yellow bile, and black bile. Patients were cut with a lancet or care fored blood or milk was dripped over a vein to encourage the leech to bite and suck from that vein. A doctor often bled a patient until they fainted. Bleeding was per stressed not righteous by doctors but also by barbers.This procedure did very little to help, but did a great theorise in regards to weakening the patient. (Krausse) Purging involved giving patients heavy doses of laxatives or emetics to expel poisons from the body. It was believed that diarrhea was relaxing the interior of the body part barf was thought to relieve tension on the arteries. (Krausse) Fortunately, in the mid-eighteen hundreds, beliefs about mental illness began to change and treatments improved. Moral management of asylums was encouraged. dementia was no longer viewed as punishment from God but as a disease of the brain, a biological occurrence that could be studied and eventually cured. This initiated a change in treatment of patients they were given decent food and clothing. They were released from their shackles and vicious confinements and were treated humanely. Women and mental illness. During thenineteenth century, women were deemed to have weaker intellectual faculties than men. It was believed that women were lacking in mental strength and, thus, were to a greater outcome susceptibl e to mental aberrations.It was in the prim succession that cult was called a female malady. These attitudes were reinforced by checkup science of that time which defined women in biological edges as naturally passive, dependent, sexually disinte be and born to be m an otherwise(prenominal)s and helpmeets to men. These beliefs severely trim womens freedom of expression and limited their access to education, employment and will power of property. Women who rebelled against these codes found themselves susceptible to being diagnosed as mad for exhibiting a across-the-board range of deviant, unnatural and unwomanly behaviors.(Jones) Medical writing at this time made it clear that doctors believed women uniquely vulnerable to mental unbalance protecting her involved regulating her sexuality and cycles. Mothers were advised to try and thwart menstruation in girls and doctors sought to regulate womens minds by regulating their bodies. Dr. Isaac Baker Brown pioneered the surgical practice of clitoridectomy as a cure for female insanity which he carried out at his head-to-head clinic in London.One of his patients was still 10 years old and the madness of several others consisted of their wish to take advantage of the new divorce act of 1857. Another young woman was brought to the clinic by her family because she had suffered great irregularities of temper, was likewise assertive in sending her visiting cards to men she want and spent much time in serious bear witnessing. (Jones) Anorexia, though prominent for many years prior, was officially recognized as a mental disease in 1873 (Ussher, 77). It flourished during the nineteenth century as women wished to symbolise their femininity.In denying food, a woman could truly be passive and bewilder a weightless accessory for her husband. The physical and spiritual ideal of anorexia also became a status symbol for many women. Working class women had to eat in order to have energy to work. Thus, only middle to velocity class women could afford to be anorexic. Cures included being admitted to an asylum where women rested and were excessively fed. The idea of the Wondering Womb also developed in this era, as madness was associated with menstruation, pregnancy, and the menopause.The womb itself was thought to wander throughout the body, playing as an enormous sponge which sucked the life-energy or intellect from vulnerable women (Ussher, 74). As a result, women became synonymous with madness, as they were pronounced to be stirred and unstable. If a woman of the Victorian era were subject to an outburst, perhaps due to elicit or frustration, she would be proclaimed insane. The word Hysteria became the general term for women with mental illness and cures included bed rest, seclusion, bland food, refraining from mental activities such as reading, daily massage, and sensory deprivation.Though these treatments do not seem too appalling, they were comparable to solitary confinement and would o ften drive a woman to further insanity. (Frick) young lady HAVISHAMS LIFE Miss Havisham was increase by her wealthy indulgent father later on her mother died when she was just a baby. She also came to inherit her fathers money after his death. As a young woman, Miss Havisham fell deeply in love with a crook named Compeyson, despite warnings from her cousin that the man was only after her money, they decided to get married.On their union day, Havisham received a letter from her groom-to-be and completed she had been betrayed and jilted. From that moment on she refused to remove her wedding dress and wears only one shoe because she was on the process of displace on the other when she received the letter. She also had all the clocks in Satis house stopped at twenty minutes to nine, the moment she realized Compeysons deception. After adopting Estelle, she isolated herself from society and remained wandering the mansion in her tattered wedding dress with the remnants of a reception that never came to be.MISS HAVISHAMS MADNESS Miss Havishams seclusion is indicative of hysteric insanity, which Conolly classifies. His definition reads There is a form of malady, more frequent among the wealthier classes than the poorer, in which discernible tangible ailments of a changeful or obstinate character stimulate associated with an infirmity of mind, at first slight and occasional, but afterward more fixed and confirmed. This form of disorder is chiefly seen in hysterical women the mind is agitated by every trifle, and every feeling is in excess, and seeks for sympathy with a morbid eagerness.It would seem as if to all the heterogeneous portions of the brain, some unrestrained energy were directed, producing endless caprices of the mind and dynamical bodily sensations they are affectionate, suspicious, amatory, cold, and repulsive by turns. Incapable of steady friendship or affection, or of adherence to any of the duties of common life, they usually, by degrees, co ncentrate their prudence on their own feelings and morbid sensations, and, laying claim to excessive sensibility, are really only regardful of themselves. (Conolly, 77)The fundamental characteristics of hysterical insanity are applicable to Miss Havisham. She has the status of wealth, a social group which Conolly considers vulnerable to hysteria. She is extremely whimsical. She is pleased with Estellas rapidly changing mood, a repeat of her own fickleness. Miss Havishams restless temper parallels her restive bodily reactions. Whenever trounce visits her, he is aware of impatient movement of her fingers (Dickens, 146) and her frequent impinging out with a stick in irritation is equivalent to ever-changing bodily sensations.To Pip as a child, Miss Havishams impatient finger movement is a cue of her whimsical demands to him. She apparently indulges Estella, but her love of her ward is egotistical. At the point of death, she is reconciled with Pip, but she cannot form steady friend ship or affection with Estella. Her withdrawal into the deserted Satis digest is, in other words, the renunciation of the duties of common life, which her wealth permits. Miss Havisham neatly fits Conollys classification. (Takei, 3) Havishams madness is not a choice. It is the effect of the congeries of various aspects in her life.The death of her mother robbed Havisham of a loving mien and a feminine role model, had she grown up with a mother, she could have been taught how to choose men intelligently, and she would have learned how to conduct births well. Growing up with a father that employs the Permissive-Indulgent parenting ardor, in which parents are high on estrus but low on discipline and control (Carson et al. 104) had made Miss Havisham accustomed to getting her counselling. This has her fixated on her wedding day, the event of her rejection and humiliation.Children reared with this type of parenting style are also observed to be manipulative, which is apparent in th e relationship between Estelle and Havisham. Also, children of these types of parents grow up to be individuals who readily enter into relationships without much thought, which is exhibited in the engagement between Compeyson and Miss Havisham. Following the unfortunate incident, Havisham has withdrawn herself from the world. The once magnificent rooms in Satis house has been reduced to ruins alter with dirt and rotting furniture.The air within is stagnant and rancid. The garden is desolated and clogged with weeds. Havisham has denounced even daylight this contributes to her illness even more. An surroundings rife with squalor, wicked memories and rotting reminders will inevitably take its toll on her already frayed sensibilities. Another contributing factor is the views of the society during that period. Spinsters were considered mentally unsound, during the 19th century doctors claimed that being without continued male interaction would cause irritability, anemia, fatigue an d fussing (Ussher).Havisham could have been initially affected by the opinions of society after she was jilted, the misadventure of facing a judgmental and hypercritical crowd could have helped clitoris Miss Havisham over the edge. Desertion on the wedding day in the Victorian social climate caused her an irrecoverable social stigma in addition to agony. Her decaying body exhibits social pressure on deserted women Her actors assistant had dropped, so that she stooped and her voice had dropped, so that she spoke low, and with a slain lull upon her altogether, she had the appearance of having dropped, body and soul, within and without, under the weight of a crushing blow.(Dickens, 107) These factors that were part of her upbringing, social and physical environment, may have contributed to the emotional imbalance of Miss Havisham. Another proof of Havishams madness not being a choice is the fact that she had sought to find a way to regain a sort of meaning and purpose to her life when she asked for a daughter she could adopt and care for. I had been shut up in these rooms a long time (I dont know how long you know what time the clocks keep here), when I told him that I wanted a little girl to rear and love, and save from my fate.I had first seen him when I sent for him to lay this place waste for me having read of him in the newspapers, before I and the world parted. He told me that he would look about him for such an orphan child. One night he brought her here asleep, and I called her Estella (Dickens, 713). This was Miss Havishams original goal, before her mental instability nudged her to manipulate Estelle into becoming a ticker-breaker that would wreck havoc on the lives of men as a kind of revenge for what happened to her. Towards the end when Estelle leaves to marry Bentley Drummle.Havisham realizes the extent of damage she had caused with Pips heartbreak. To see her with her white hair and her wear face kneeling at my feet, gave me shock through all my frame. I entreated her to rise, and got my arms about her to help her up but she only press that hand of mine which was nearest to her grasp, and hung her head over it and wept (Dickens, 709) Until you spoke to her the other day, and until I see in you a looking-glass that showed me what I once mat myself, I did not know what I had do. What have I through with(p) What have I done And so again, twenty, fifty times over, What had she done (Dickens, 710) Havishams press out remorse and guilt when she realizes that Pip has been through the same heartache she has experienced is proof that the perverse influence she provided Estelle was not done because she deliberately chose it, rather, she had reached emotional instability because of the events in her life that enabled her to do such actions. As soon as she realized the effect it had on Pip, she was scare and begged forgiveness. She recognizes that she has tormented Pip, whose heart is as vulnerable as her own.Havisham says, I am not all stone (Dickens, 705), her sympathy and the kindness of a human heart still remains. By her ethical awakening, she recovers her sanity for a utterly while. Havishams madness was not a choice the events in her life, the environment she lived in, the social interactions she subjected herself too, and her personal flaws, all of these played a part in her mental fragility. Miss Havisham had truly loved Compeyson. This is apparent in one of her conversations with Pip, Havisham exclaims, Ill tell you, what real love is.It is blind devotion, unquestioning self-humiliation, utter submission, trust and belief against yourself and against the whole world, giving up your whole heart and soul to the smiter as I did (Dickens, 426). The intense passion and complete loyalty she had mat up for Compeyson corresponds to the utter heartbreak she went through and the unbearable torment she felt over his betrayal. This was the principal event that led to her insanity, unable to cope sh e manages to operate only by retreating into her own mind and withdrawing from the difficulty of moving on with a normal life.She believed her mental illness was necessary for her existence. Works Cited Carson, C. , Butcher, J. , Mineka, S. kinky Psychology and Modern life 11th edition (Needham Heights, MA), 2000. release Dickens, Charles. Great Expectations, Planet PDF format (online publication Planet PDF). Web Ussher, Jane M. Womens Madness Misogyny or Mental Illness? (Ameherst, Ma University of mamma Press), 1991. scar Takei, Akiko. Miss Havisham and Victorian Psychiatry, (PDF format) . Web Conolly, John.On Some of the Forms of Insanity (London), 1850. Print. Jones, Claire. Women and madness, Herstoria magazine (Jones5 Publishing Limited) . Web Goldberg, Ann. Sex, Religion, and the Making of Modern Madness (New York Oxford University Press), 1999. Print Summary Mental illness during the 19th century had initially been attributed to built-in malevolence or punishment from G od it was during the mid-eighteen hundreds that doctors have begun to view it as a disease of the brain, a biological occurrence that could be treated.During the Victorian Era it was believed that females were more susceptible to mental imbalance because of their weaker minds. Society situated that the roles of women should be strictly confined to household and they must all be under the support of men. Miss Havishams madness was not a choice. It was a result of the conglomeration of various aspects of her life the environment she lived in, the family she grew up with, the events she had been through, the society she is part of and the personal flaws she had.All of these have played a role in her madness. The breaking point had been the abandonment and betrayal of her fiance Compeyson, whom she loved deeply. In her devastation she proceeds to let her life swan around the wedding day she never had. Havisham wanders the ruined halls of her Satis home wearable the yellowed wedding d ress she refuses to take off and using only one shoe because she was in the process of putting on the other pair when she received the letter from Compeyson.She also had all the clocks in her home stopped twenty minutes to nine- the moment she realized she was betrayed. She adopt a girl named Estelle and proceeded to influence her to become a cold and merciless girl to wreak havoc in mens lives. She saw this as a type of revenge to all men for the pain shes been through. Towards the end of the book Havisham regains sanity for a short while after realizing the pain of heartbreak Pip has been through because of her machinations. Guilty and remorseful, she begs Pip for forgiveness and realizes her mistake.

‘Raw’ by Scott Monk Essay

Raw is a wise written by an Australian author Scott monk for young teenagers to seek an alternative approach to the juvenile justice system, one that supports and encourages young offenders to beget do responsibility for their actions. Monk uses significant episodes, contrast in characterisation and a range of language techniques to show the central character journey as he learns to take responsibility for himself. Monks plot is based on a theme which is action packed with violent episodes such as Tyson and his cabal attacking Brett and cutting of all of his hair. As intumesce, it is based on a whop triangle where Brett is put in surrounded by his new love interest Caitlyn and his ex-girlfriend Rebecca. It also follows a journey theme where Brett changes once he travelled an 800 km journey from Sydney to the Farm. The plot is episodic and highlights the change in Brett. Episodes which show this change and that it is sometimes difficult for him include, walking away from rub bish Mr Douglass, not letting his anger control him, hed befogged one fight but won anotherAs hygienic as apologising to Caitlyn realising that he was wrong and wanting to fix his mistakes, And hed learnt that the hard way that love couldnt be owned peerless main character was utilise to show the theme of a trouble individual and societys way of dealing with them. Monk writes in third individual but with Bretts perspective. He also used many secondary characters who are a part of Bretts journey such as, his love interest Caitlyn, friends Josh, surface-to-air missile, Robbie and enemy Tyson. Monk also smartly contrasted characters to highlight the aspects of society, for example, Sam treats the kids like ruler citizens, not criminals and tries to help them build their lives, which is contrast to Mr Douglass who makes assumptions about Brett and all of the boys at the prove, not treating them as normal citizens of society and not allowing them to show that large number can change.Monk also used Bretts developing relationships to show his slow growth into someone who has something to offer society. For example, his relationship with Caitlyn teaches him that you need to treat people with love and find to receive it, he also learnt that other peoples wants and postulate are just as important as his own. His relationship with pull the leg of allows him to understand that someone will always have it worse therefore you and that whatever is happening only you can control and change your future. hardly remember, Brett, only you can change your life. The language used in the unfermented is directed at Monks youth audience. He uses colloquial language, when Brett calls the police (pigs) as well as lots of direct speech to show the interactions between Brett and the other characters, (Josh) I saw you perving at Caitlyn (Brett) what Is that her name?Monk uses descriptive language builds up the imagery of his characters, The man looked like an old pun ch or one of those guys who drive cattle, a stockman As well as the settings used, imagery is sometimes very symbolic for example, Brett leaves Sydney and arrives at the farm in a paddy wagon then 3 months subsequent leaves back to Sydney in the paddy wagon but as a changed man. Monks presentation of the farm as a juvenile detention plaza shows his audience another side of this issue. There is minimal security, few rules where Sam and Mary treat everyone as individuals dont call Brett a no-hopper Monks theme of the individual being responsible for his/her own actions is shown well.His characters show that when they make abominable decisions there are repercussions. For example, Rebeccas decisions ruined her future, and Tysons stinking choices ends him in jail. At the take of the novel Brett was consistently making bad choices but by the end of the novel Brett is making good choices, which is shown when he walks away from Mr Douglass. The epilogue of the novel shows the result of this idea when Sam asks if hes learned anything and he realises he has, lots of stuff, like friendship. Trust. Love. And loss. unconstipated though he is going back to Sydney, in the same paddy wagon he came in, to go to a proper detention centre,Monk shows that Brett has changed through his thoughts at the end, He was young and he was going to start again Scott Monk wanted his readers to know that if you are in a bad situation only you can change that, but having people around you who offer a second chance can be vital to prove that you can be a good person and you can change for the better.

Adopting Children by Same Sex Parent Essay

People in partnership say that every unmatched is constitute, they brace equate right and freedom. However in case of makeing children, commonwealth believe that very(prenominal) agitate p atomic number 18nts argon abnormal to adopting children. Some deal in family against them to adopting scarce in that respect be legion(predicate) said(prenominal) provoke couples who be seeking to adopt children. The researcher of homo fireuality found that galore(postnominal) citizenry still do not reveal their sexual druthers to others.Also, identical sex couples are not acceptable from some plurality in society, gibe to www. gay-adoption. s. On the contrast, some people believe that alike sex adoption is normal and it should be acceptable, accord to the right human universe campaign, a national gay and lesbian advocacy group. Although in that location are many people against alike sex couple to adopting children, same sex couples should be allowed to adopt children b ecause they declare equal rights and they great deal be exhaustively parents for a child who lacks slam and home. Moreover, children in the get together State of America and many countries around the world are waiting for adoption. on that point are most 520,000 children in welfare, according to the North Ameri depose Council on Adoptable Children in St. Paul. In addition there have 120,000 are available for adoption, but but 50,000 find permanent homes each year. However, although same sex couples want to adopt children, they are against by straight person parents for several reasons including it is unnatural to allowed same sex to be a parent, same sex parents female genitalianot give perceptual constancy to children and most people believed that only straight parents crowd out be rock-steady parents. Firstly, it is unnatural to allow transgender couples to be a parent.They cannot be total parents. Also, it is not safe for children to live with same sex parents. T he surpass purlieu for thoroughly-being of children is a household with a vex and father because children should have a role model. Adopting by same sex parents can do to children. For instance, children who is overturnd in a homosexual household are importantly more likely to be homosexual themselves because they have only one role model in one gender, and get involved in homosexual behavior than children raised in heterosexual households, according to a research in the US (University of Illinois Law Review, 1997).In a exact published in the January 1996 issue of Developmental Psychology, London researchers Susan Golombok and Fiona Tasker found that it risk of exposure for children that live with same sex parents. However, the sexual orientation of parents has no bias on the sexual orientation of their children and that children of lesbian and same sex parents are not more likely than any other children to grow up to be homosexual, according to Children of gay fathers, G ay and Lesbian Parents (p. 9-57) In addition, children can manage their life to be what they want to be by themselves, moreover they are raised by homosexual parents but it is not agree that they may have the same behavior as their same sex parents. Moreover, same sex parents can give a responsibility and love to children as well as a heterosexual because they are a human who can teach and give love to a child. As such, it would be wrong to deny same sex parents to adopt children.Also, replete(p) parenting is not controlled by sexual orientation, same sex parents can validate children and give love to them that show they can be a faithful parent same as a heterosexual. Secondly, the reason why people believe same sex parents should not be allowed to adopt is perceptual constancy, so it is important in raising an emotionally and mentally healthy child. The manner to children grow up happily may need a role model, so children need a role model of both genders that are male and female in order to develop a properly. If children raise in homosexual household, it influence to children will lacks information of other gender.Childrens primary role models are his or her parents that cause delivery a heterosexual up in a homosexual household can gives children a misrepresented view of sexuality. Homosexual couples simply cannot give the stability that heterosexual parents can give to children. Although most people believe that bringing a heterosexual child up by same sex parents give them a distorted view of sexuality, some babies are innate(p) with a predisposition to homosexuality and their upbringing will not prompt their sexuality. Almost of homosexuals couples do not want to force children to be homosexual like them.According to Major associations of mental health professionals in the coupled stated of America, same sex parents are not an unfit and exposed as heterosexual parents that they lead children are as happily, healthy and well adjusted as a ch ild who is raised by heterosexual parents. In addition, a studies shows that children raised by single heterosexual parents have more difficulties than children who have same sex parents. Moreover the study shows that children did improve in moderation, self-esteem, and had less psychosocial difficulties at home and at school, according to the study of Same-Sex Parents Raise Well-Adjusted Kids.The last reason is widely agreed that only heterosexual parents can be a good parent and they are appropriate to give love, warm, and home to children. Children should have opportunities to thrive in heterosexual parents with a mother and father based family. Heterosexual parents are the best because a child should be raised in loving, well-disciplined homes where children have good role models from their heterosexual parents, excessively avoiding children grow up to be a homosexual, according to study of gender identity disorder and psychosexual problems in children and adolescents.In addit ion, avoiding from criminal because homosexuals are more likely to molest children, such as rape them. It is danger to childrens life and causes many troubles to society. However, there are about 500,000 children in welfare nationally in the United state and about 100,000 children need to be adopted. So it is shows thousands of children lacks a permanent home and lacks love from parents, according to the statistics of the study of critical shortage of foster and foster parents in the United States.If they are only allowed heterosexual parents in adoption, the child who lives in foster care will lacks family and as in Florida more than 2,000 children in welfare are waiting for adoption according to the state of Floridas statistics. In addition, there are not adequacy heterosexual parents who are interested in adoption and foster care. There are some arguments of adopting children by same sex parents because most people feel that only traditional homes with a father and a mother are appropriate and have equal right as heterosexual parents to adopt children, according to issue about facts on gay adoption.However, society is change that leads everyone has equal rights. Therefore same sex parents are human being who should be allowed to adopt children. All people should have equal rights because the child in same sex family appear to be normal, and also same sex parents are not appear to harm child, according to Homosexuality and Family Relations. If homosexual parents can support their children, same sex couples can be as good parents as heterosexual parents. As such, same sex parents are the same as other people who can support children, such as, they give love to children, pay taxes, go to work.It shows that being homosexual is not a mental disorder. In addition, nowadays there are thousands children have no permanent homes, and they are waiting for adoption. It is shows that same sex parents are one of those who help children to have love and home. Therefore, people should not determine only about sexuality of those who want to adopt children. As Mary Bonauto of Boston-based same sex couples Avocates and defenders said that, Sexual orientation is not the issue, ability of parent is issue.

Odyssey Review/Essay Questions Essay

1.What aspects of social and political liveliness in homing pigeonic times are reflected in the Odyssey? =The aspects in the social and political life in Homeric times that are reflected in the Odyssey are the lead and hierarchy. These are depicted by kings, contendriors and peasants who sometimes live un- zepic simple life.Other than that it shows the finale of the Greeks wherein if you provide court a lady,you should bring gifts. 2.What is the purpose of the many an(prenominal) tot whollyyusion to the novel roughly the theatercoming of Agamememnon? =Agamemnon had an unhappy takings.He was either winded by course and landed in the country of Aegisthos, or he came domicil to his own land to find Aegisthuswaiting for him. In either case, Aegisthus had become the lover of Clytemnestra, and the two together murdered Agamemnon and Cassandra shortly after their arrival. Aegisthus and Clytemnestra then rule Agamemnons kingdom, scarcely were eventu altogethery eliminatee d by Agamemnons son, Orestes (or by Orestes and Electra in some accounts). The homecoming of Agamemnon and its aftermath were favorite subjects for Greek tragedy.Basic onlyy, his unhappy homecoming was used to foretell the possibly unhappy homecoming awaiting the unhappy friend Odysseyus, although his wife does not marry any of the suitors, and his homecoming ends up world a relatively happy one.3.What outstanding personal qualities en adequate to(p) Odysseus to stretch out all his dangerous adventures and to surmount all obstacles to return home safely and regain his old staus? = The outstanding qualities that I think Odysseus had were that he was his intelligence, his strength, and he was very caring. His best quality is that he is very intelligent. He is able to use his bear in mind to find solutions to problems, outsmart people, and to just use his mind for many different problems. For example when the water flea asked Odysseus what his pattern was and he replied by saying, Nobody.And so when Odysseus poked the daphnia with the sharp blade and he started let loose the former(a)(a) Cyclopes asked him who was br each(prenominal)ing him and he replied, Nobody is stomaching me, so they just ignored him. Another of his Odysseus outstanding qualities was his strength. This helped him in war and to shape supplies. The last of his outstanding qualities was his caring towards his crew. He tried to keep all of them safe as long as he could. He authentically cared for his crew and he was devastated when his crew got killed. These were his best qualities.4.What are some Odysseus weaknesses?=Odysseus greatest weakness is his pride. Although pride suffer be a good thing, he is claimed to possess too a great deal of it. This is shown in an act of hubris in allow nine of the Odyssey, when Odysseus taunts the Cyclops Polyphemus after blinding him, which leads Odysseus to be cursed by Poseidon. =Odysseus curiousity could withal be considered a weakness. On t he island of the Cyclopes, Odysseus fell into temptation to baffle in the Cyclopess cave to see what the Cyclopes looked alike(p) (Polyphemus). This left 6 of his custody dead. 5.What is the significance of the blind bard,Demodecus,who entertains at the banquets of poove Alcinous to historians? =In the Odyssey by Homer, Demodocus is a poet who often visits the court of Alcinous, king of the Phaeacians on the island of Scherie. DuringOdysseus stay on Scherie, Demodocus performs three narrative songs.In short Demodocus represents Homer in the story.6.What role does genus Athene play in the Odyssey?Why is she often considered its weighty female character? =Athena is the patroness of Odysseus or most of all she loves his mind. Odysseus is a character that solves his difficulties not done strength or other god given humbugnt he sticks his time and thinks the problem through with(predicate) because Athena is a goddess of wisdom she would be partial to a hero like odysseus. =Ath ena is considered the main female character in Homers Odyssey is because Athena is always mentioned by Homer divinely step in with Odysseus path e.g.Athena asks Zeus to release Odysseus from Calypsos island of Ogygia and so he sends Hermes to order Calypso in Book 6, Athena is the condition both Odysseus and Nausicaa cross paths by the river bed. 7.What does the dramatic climax of Odyssey take slur?Is this before or after reunion of Odysseus and Penelope?Why? =In my understanding each book contais different dramatic climax that for me I have some examples of it like when he finally reveals that he isnt a beggar like Athena disguised him to be but rather Odysseus that has returned.The day that he killed all the suitors.The day that all his men died and so many more. 8.Who is Odysseuss enemy and why?=I believe it was indeed Poseidon. The reason being that he blinded the Cyclops (Polyphemus).The story went that, term they were on the island,Odysseus named himself Nobody so that wh en the Cyclops shout out for help, he claimed that Nobody had blinded him, making his comrades think it was a penalty from the gods. Odysseuss mistake was to call seat from his retreating ship his true name. The Cyclops was the of Poseidon, who sought revenge. =Other enemies are the suitors of Penelope.The suitors essentialed to get Odysseus throne of worthy king of Ithaca and became powerful. 9.What is Telemachus problem?=He hasnt seen his father in 20 years,since the day of his birth.He was confident enough the his father is still alive and also the suitors are eating up his fathers land and want to marry his mother.10.Why is Odysseus choice to raid the land of the Cicones,Ismaerus.a bad choice? What ruling do you get of Odysseus from this encounter? = Odysseus and his men sack the city of Ismarus, kill many of the men and take their wives and booty, which include wine, money, and sheep. Odysseus spares Maron, a priest of apollo, who gives him much concentrated wine, 7 talen ts of gold, and a bowl of silver. Odysseus tells his men to return to the ship, but they do not obey, instead reveling in their spoils. Meanwhile, some of the Cicones had moved and warned their brothers who brought many troops with chariots to fight off the Greeks. They end up killing about 70 men, (6 from each ship), before Odysseus and his men retreat. Odysseuss ship was blown off onto an island that had a cyclops that Odysseus do blind by ramming a hot log into the cyclops eye. He also escaped penalisation from Poseidon the Cyclops father by claiming that he was Nobody.It is bad enough to do such things for your survival.11.What do you think is Odysseus welt action of his wanderings and why? =Odysseus worst action of his wanderings is when he was in One-eye Cyclopes island. It is because aside from he hurt Polyphemus eye, he made a wrong move that prolonged his trip back to Ithaca. Though he just made it because he wants to escape in Polyphemus cave, still his pride leads th em into their long journey back home. When Odysseus and his men are clearly safe away from the island, Odysseus brags about his exploit. He shouts his name and unwisely gave away his identity to Polyphemus.With that Polyphemus called upon his father, Poseidon, to punish the man who had harmed him. That incident hurt Odysseus more than losing a few men, because Poseidon made his travel home protracted than he expected. He faces different struggles which brought them into danger and sad to say, he is the only one left because his men died. Nonetheless, Odysseus survived all that happened to him. His courage, wits, and endurance enabled him to come through each and every difficulty and arrive home safely.After 2 decades of being away from Ithaca and longing for his wife and son, Goddess Athena let him go back to his home and be with his wife and son. 12.Why is the Odyssey a story use up by so many after years and years? = I think its because the Odyssey is almost a template that sets up our lives today. In this piece of literature, the Greeks value so much on good hospitality, which is important in our society. Everything can lead back to the Odyssey. Our tendon is called the Achilles Tendon linking back to a great hero who fought in the Trojan War, some lyrics were excite and taken from the Odyssey, Apollo 13 is taken on from Odyssey.=Also, a lot of characters take up after the Odyssey. Think about the characteristics Odysseus have and compare them to the characters our heroes in our society have. What are the similarities and differences? Even our damsel in distress is inspired by Penelope. Of course the sirens, the goddesses are all a template of how our female characters should be.The Odyssey marks the get goingning of a lot of things, and its also a great story to read.13.Why is Odysseus looked to as a powerful representation of the mythologic hero? =because he was very brave and a good leader. He helped his men escape many situations including the cyc lops. he has all the qulities of a hero. He slept with Circe so that his men would be turned back into gays. He made many sacrifices to help those in need.Being a hero comes with great responsibilities and duties.You will do anything just to make your countrymen happy. 14.In what ways are the Iliad and the Odyssey similar?In what way do they differ? Similarities Both are attributed to Homer. Both begin with an evocation of the Muse. They both take place over the course of 10 years. They both begin in medias res, or in the middle of things. The Iliad opens up in the last couple weeks of the final year of the war the Odyssey opens up with Telemachus searching for news of his father, and then we first learn of Odysseus through flashbacks while he is being held captive by Calypsowhich was actually most the middle of his journey. They both use dactylic hexameter. Many of the same characters can be found in both poems.DifferencesThe Iliad is about a 10-year war fought between the Achae ans (Greeks) and the Trojans the Odyssey is about the 20-year journey home of the hero Odysseus after the Trojan War. Achilles is one of the leading characters in the Iliad Odysseus is the leading character in the Odyssey. The Iliad is a poem congress the tale of many (Achilles, Hector, the gods, etc.), while the Odyssey is primarily the tale of Odysseus. Menis, or the wrath of Achilles, is the main focal point and one of some(prenominal) themes in the Iliad Nostos, or homecoming, is the main focal point and one of some(prenominal) themes in the Odyssey. In the Iliad, the gods are portrayed as pretty deceptive, temperamental, backstabbing gods theres a lot of sneaking around behind each others backs to aid one side over the other (Hera wanted the Achaeans to be triumphant, but Zeus tried to remain neutral), several(prenominal) of the gods conspired to put Zeus to sleep so they could help the Achaeans win, and thebattlefield is essentially one giant chess board for them, with mo rtals as their pawns. In the Odyssey, the gods depend a subaltern more benevolent (Athena supports Odysseus and tries to assist him whenever she can, and they all exclude Poseidonwould like to see Odysseus return to Ithaca) and they seem more unified and well-behaved in their views on how things (particularly Odysseus making it home) should be handled. Even though Athena was Odysseus staunchest supporter, she did not try to retaliate against Poseidon when he made Odysseus journey all the harder and even longer. In the Iliad, the gods were more actively involved in the personal business of mortals than they were in the Odyssey. In fact, there were numerous occasions where they actually took human form so they could go out onto the battlefield. In the Odyssey, there was little intervention, and usually only when it was asked for. The Iliad takes place in one location troy in the Odyssey, Odysseus visits numerous places in his journey home. 15.Explain how Homer uses chronology in telling the story of Odysseus? =Theres a difference between the chronological order of events in the movie and in the story.In the movie it started the day that Telemachus was born(p) and Odysseus was invited to fight in the war.After the war ,his journey in sailing home have begun in sailing different islands and places like the One-eyed giants cave,Meeting the pilot of the wind,Land of the bewitching queen,Visit to the underworld,Island of temptation,Calypsos kingdom and landing to the Island of Scheria,home of the Phaeacians.In the movie there were no flashbacks or throwbacks.The events were continuous unlike in the book the past events were told when Odysseus arrived at Scheria and told all his journeys and trials.

My Aim in Life Essay

need is the target which we lack to achieve towards which our physical and mental abilities are focused. disembodied spirit is the period which starts from the time of birth and ends at death. People have their take in strength, culture and liking. Depending upon these elements sight have different kinds of aims in life sentence. For example, some people are doctors, engineers, Charter Accountants, pilots, teachers and many more. Our life is too short so we have to strive to attain our aim with all our hard work. The chief(prenominal) objective for achieving the aim is to get material pleasures, mental happiness as well as satisfaction. Once a person achieves his aim he can live a prosperous life.My aim in life is to become a successful gynecologist. Gynecologist is a doctor which deals with the health of female reproductive system. To accomplish this aim I am prep to study +2 in India taking Science as the of import subject after I attend my SLC examinations. After that I want to become a medical student of a top university of gynecology. I will attend different kinds of trainings, research and programs. This profession is also regard all over the world. I have been inspired by unrivaled of the top gynecologist of Nepal, Dr. Supatra Koirala. The present scenario of the reproductive healthcare of the women in Nepal in overall is not satisfactory. Due to this, the maternal and child mortality site of our country is very high. I would conduct different awareness programs in the remote areas of our country and provide free medical services to the economically back warded people and be a helping hand for the evolution of my country.Thus, once I achieve my aim I would help to correct the reproductive and sexual healthcare of the women countrywide. I want to make the women of my indian lodge healthier and happier. By becoming a gynecologist, I would live a prosperous life and be a productive and global citizen of my country.

Internet and Cell Phone

What did you find most interesting and/or surprising? What information rattling stood out for you when exploreing this topic &038 why? Whats the most important subject we, your audience, should take away from your research? -Originally the kiosk surround served as a mutilateicial document for business management. Now, cubicle phones serve as a tool for affectionate connection, in other words, managing social relationships. Across qualitative and numeric studies, maprs of the cell phone all report employ their phone for social purposes.However, scholars start out argued the cell phone might actually serve as a tool for social isolation (Bugeja, 2005). On the other hand, the cell phone has been argued to function as a social connection device, oddly among teens (Ling, 1999a). Therefore, the social use of cell phones has proven to be a large area for communication research, with researchers exploring various ways in which cell phone use affects social interaction, both is olating and connecting involved persons. -Although observational research shows that most cell hone users retreat from social settings when they are using the cell phone in a public place (Ling, 1999b), findings too suggest that cell phone users use the cell phone in public spaces as a form of exclusion (Bugeja, 2005 Ling, 2002). The survey prove that 13% of surveyed adults said they had used their phones to look busy, so they wouldnt have to talk with others. That percentage more than doubled among young adults aged 18 to 29 years, 30% of whom said theyd faked cell phone use as an emptyance mechanism.Only 2% of the oldest (65 and older) respondents describe using cell phones to avoid dealing with others. unplugging may actually improve your social interactions. As Healthland reported last year, many people would argue that turning your phone off is a gesture of intimacy and affection for the people around you -The implications of this lead are not only empirical, but serve to demonstrate the dangers that vigorous communication technologies may pose if not used meetly. Discretion of cell phone use is even evident in current extract laws that prohibit drivers from talking on the phone while driving.This alone testifies to the dominance risk of danger that interactive mobile technologies pose for its users. A assertable solution is to make users more aware of the effect of these mobile technologies on their attention, not only to strangers but even their surroundings. As proper etiquette exists for lucre behavior, perhaps we ought to develop a social code of behavior for proper cell phone usage. http//healthland. time. com/2011/08/15/survey-1-in-8-fake-using-their-cell-phone-to-avoid-talking-to-others/

Bringing Adam Home Essay

rescue go game business firm review examines the story of the decades-long investigating into the abduction and murder of 6-year-old turn Walsh. The police investigating took 27 years to prove guilt of the serial humansation killer, Ottis Toole, who made binary confessions to the murder. The book is write by the experienced detective writer Les Standiford with the help of the retired detective Joe Matthews, who last implant evidence of Tooles committing the murder 27 years afterwards. The part of disco biscuit Walsh has influenced the American ball club in the way that general assemblys were made protecting children, and practices were adopted helping knock missing and potentially abducted children. Key words abduction, evidence, investigation, kidnapping, murder.speech raptus Home Book ReviewStandiford, L., & Matthews, J. (2011).Bringing exaltation home The abduction that changed America. New York, NY harpist Collins. ISBN9780061983900.Bringing spell Home is the story of the decades-long investigation into the abduction and murder of 6-year-old Adam Walsh who missed from a local Sears in Hollywood, Florida, on July 27, 1981. The police investigation took 27 years to prove guilt of the serial killer, Ottis Toole, who made multiple confessions to the murder yet the Hollywood, FL, police subdivision did not believe him and failed to bat any of evidences that had been found. The abduction of Adam Walshblew peoples minds and undermined their sense of protection. The American smart set has never been the same ever since pargonnts did not let their kids play unaccompanied outside, nor did their ever say Be home by dark a child could be left nowhere unsupervised. It was Adams family wondering(a) luck that at that time, there were no Amber Alerts and no internal data base for crimes against children.Adams parents, tin can and Rev Walsh, bent on(p) backwards to change the situation. They became renowned crime fightingers, propelle d the passage of the 1982 Missing Children Act, and John Walsh became a host of the television program Americas near Wanted (Standiford2011). Adam Walshs kidnapping was not only the around consequential facial expressionin American history of missing children that changed the corresponding legislature save to a fault the most(prenominal) famous one. Many people lock up remember themselves being kids and watching it on the news (Martin, 2011). However, the details of the case are not as well-known as they should be wedded the wipeage in the media.The more emotional side of the story, through the eyeball of the Walsh family, is rendered in Tears of Ragewritten by John Walsh (Scott, 2011). The puzzle of the botched investigation that ran over almost three decades was work ond by the retired Miami detective Joe Matthews and written down by the acclaimed writer Les Standiford, the author of 9 fiction novels and 6 non-fiction books (Standiford, 2001).The authors open their card s in the actually beginning of the book and inscribe the killer, Ottis Toole, right in the second chapter. Toole was a low IQ vagrant who set fires and assaulted people to relieve his psychological pressure. From chapter 2 to 4, the authorsgive a slender recount of the work of Hollywood detective Hoffman who could not organize his work so not to lose important clues and evidence and who was not truly keen on the idea that Toole was the killer. According toMatthews, Hoffman is portrayed as a moody and self-contained investigator who looked desire a guy who disapproved of most things on general principle (Standiford, 2001). Apart from disregarded leads and lost evidences, Hoffman also treated Adams parents carelessly not bothering to inform them that their promoter Jimmy Campbell, who was prime suspect, had been cleared.For many years John and RevWalsh original no information from the police as for the investigation of their sons murder. Matthews felt that it was exceedingly insensitive on the part of Hoffman. Together with unexploited enough forensic methods, the case of Adam Walsh advanced by incognoscible pace. As Reve Walsh put it It was a sad thing for this country that the fight had to be led by two broken-down parents of a hit child(Standiford, 2001). The authors underscore that it could not be said that the Hollywood discussion section was incompetent. Rather that the case was too difficult, and Detective Hoffman turned out to be too snobbish not only to ask for help but also to accept help from Joe Matthews when he offered it not once. Hoffman was too uncrystallized and ill-equipped for such mind-bogging case (Standiford, 2001).Det. Serg. Matthews was a lie detector serious and an experiences homicide detective and, being hired by the Hollywood, Fl, Police Department, he was very interested by the case and was ready to use his knowledge to solve the case.Among other things, the difference in approaches of two detectives was that Hoffma n was obsessed with decideing sensible evidences linking Toole to the Adams murder while Matthews believed that circumstantial evidence could start do in some cases. That meticulous recount of all palpable mistakes of the Hollywood, Fl, police department and the detailed translation of their daily working liveness had its aim in showing that detectives work is far from the glamorized TV series. Doing on a daily basis such boring chores as distinct for a person who moved and did not leave the new address, or surveilling a suspect for many days, exhaust detectives, and the not very consecrated ones let things slide (Standiford, 2011).Standiford and Matthews seem to mention every lead that was not followed, and every report that was incomplete or level(p) falsified.Matthews blames the manner of scrutiny when the suspect was let speak without asking necessary questions, and he found the witness who was consistently ignored by Hoffman. The most shocking omission, the proofreade r may consider, was the neglect of the repeated confessions by Toole with a graphic description of the whole process of abduction, murdering, sodomizing, and decapitating of Adam Walsh and the subsequent dismembering and setting ablaze his body. Toole even gave a sensational interview to Jacksonville Times Union where he repeated his confession to the murder of Adam Walsh (Standiford, 2011). Chapters 5 to 6 focus on Matthewss account of how he proceeded with the investigation. It became possible only after Hoffman was transferred to the patrol Division in 1994 (Standiford, 2011). Matthews spent two years and nine months reviewing the case and adding new materials. In the end,Matthews had multiple eyewitness identification of Toole taking Adam from Sears, twenty-five independent confessions to the crime made by Ottis Toole, and most important of all missed by previous investigators sodium thiopental images of machete and luminal outline of a childs face on the cover of Tooles Cadi llac.It finally proved Ottis Toole to be the man who committed the crime. The runner part of the book does not make an easy reading. When Toole gives his numerous confessions to several(a) detectives all the same details of the murder, rape, and dismembering are repeated ad nauseam, without adding anything new. Because of it, for those readers who like genuine crime stories, the book may seem quite slow. Standiford and Matthews were extremely repetitive in details of the crime itself, its prolonged investigation, the history tail the suspects, and descriptions of Tooles perversions. However, the authors rather had in mind to show how the process of investigation can be dragged for years due to the inability of the police to find hard evidence for the already confessed crime. Standiford, who is an experienced detective writer with a number of narrative non-fiction stories under his belt, narrates dryly and matter-of-factly, which contributes to the authentic feel of the blood- chilling story. condescension waving their incompetence, Matthews provides a scrupulous evidence of the Hollywood, Fla., police departments negligence, thus making it difficult to believe that behind such an untrained behavior may be anything other than a conspiracy to cover up its incompetence. The authorsaim seems to lay in proving two points. Firstly, the case could accept been solved within two years, when Ottis Toole was arrested for arson and confessed repeatedly to the murder of Adam Walsh saying that he was very, very sorry that he did it (Standiford, 2011). Secondly, the police department of Hollywood, FL, had a chance to solve the case quickly, had they let do it to Det. Serg. Matthews.Bringing Adam Home is a gruesome story of justice finally served two decades too late. By that time, though, Ottis Toole had died in prison. And our society has changed. Now kids are warned about strangers. No one leaves their kids in the toy area and goes shop anymore. Lawenforcement has transformed its practices to better protect children. Public places have adopted law Adam, a powerful search tool for lost and potentially kidnapped children ( enter Adam, n.d.). Code Adam is a predecessor to Amber Alert, a network of notifications to the public through urgent bulletins on television and radio.ReferencesCode Adam.(n.d.). The National pertain for missing &exploited children. Retrieved from http//www.missingkids.com/CodeAdam Martin, C. (2011, February 09). Book Review Bringing Adam home by Les StandifordWeb log post.Retrievedfromhttp//www.chaoticcompendiums.com/2011/02/book-review-bringing-adam-home-by-les.html Scott, M. (2011, February 26). Bringing Adam home offers beardown(prenominal) proof in the 1981 murder of Adam Walsh. Cleveland.com. Retrieved fromhttp//www.cleveland.com/books/index.ssf/2011/02/bringing_adam_home_offers_stro.html Standiford, L. (2001). BiographyWeb log post.Retrieved from http//www.les-standiford.com/Pages/Biography.html Standiford, L., & Matthews, J. (2011).Bringing Adam home The abduction that changed America. New York, NY Harper Collins. E-book

The Color Purple

English 102 24 April 2007 Awakening of an Abused muliebrity The Color violet is set in the rural south and told by dint of a series of garner written by the protagonist, Celie, chronicling her journey from infliction and humiliation to triumph and rebirth. Throughout most of her breeding she has been tempered as a servant. Her that worth as a charr is for cooking, cleaning, fetching care of the family and fulfilling mens desires. She has n for ever been taught how to love or be loved and throughout most of the novel Celie is abused and very infelicitous exclusively she gauges that this is the modal value women are supposed to live.It is not until she lets women into her flavour, which lead Celie to her epiphevery, that she realizes that she deserves more(prenominal) out of her life and that she is worthy of honor. Through sharing relationships with them, Celie sees how women should be treated from another perspective than what she has been taught by her family. Celies life is one of campaign and despair. The first line of the story is what her step cause told her when she was simply xiv years old, after raping and impregnating her. This statement is so profound that it formulates why she is so scared of men her whole life and emotionless to the things that are do to her.The line states, You f alone apart not never say no frame but God. Itd kill your mammy. (Walker, 1). It is then that she starts writing to God. She can not tell anybody what has happened to her, not even her sister, Nettie, whom she is closest to at the period. Nettie wouldnt even understand, she thinks, because she is younger then Celie and Celie doesnt even understand what is going on. Celie feels the altogether way to go through life is to remain silent and persevere. Her only payoff is through her letters to God. Celies stepfather, Fonso, then marries Celie off to a widower who needs a mother for his children and someone to do the housework.The widower, Mr. ___, o riginally came for Netties hand in marriage but Fonzo refused. Fonso gives Celie to Mr. ____ instead, telling him She aint freshShe spoiled. Twice. , then he goes on to say, She ugly. But she aint no stranger to hard work. (Walker, 8). This is where Celies self worth is real shown to her. She feels that all she is good for is the hard work she accomplishes inside the home. The way the pot closest to her talk about her in combination with all the dreadful things that has happened to Celie mends her feel worthless. She has very little self-worth and self-esteem.She is a product of excessive personal and mental abuse. The oppressive brutality of her life continues when she marries Mr. ___, who beats her and subjects her to a life of domestic servitude. Nettie later decides to run away from Fonsos house because of the regular abuse towards her and decides to move in with Celie and Mr. ___. Nettie sees that life is not that much better at Celies house and after Mr. ____ tries to r ape her she decides that she must extend there, also. Consequently, Fonso tells Celie that he will make certain(a) her and Nettie never speak again.For galore(postnominal) years after Nettie left she writes Celie letters, but Fonzo hides them before Nettie gets them. Fonso tries to break the only bond Celie had that brought her any happiness. It is not until Celie lets women into her life, once again, that her thinking starts to change. The first charwoman she becomes close to is her daughter- in- law, Sofia. Sofia is very strong and fierce, the total opposite of Celie, and she was not to be ruled over by her husband or anyone else. Sofia fights back when her husband, Harpo (Mr. s Son), tries to rule her with an iron fist.Sofia refuses to be oppressed condescension the prejudiced ordination of the 1930s south in which they all live. Sofia in solaces in Celie a cleanfound strength. Celie is so immersed in conquering, she accepts the point of view of Mr. she advises Harpo to beat Sofia. Thus, she agrees with her oppressor in the cerebration that a woman should only obey, work and be silent. After this upshot of deep humiliation, Celie has the first serious conversation in the book. Sofia comes to see her, furious, and Celie has to explain her attitude. She discovers she is jealous of Sofias capacity to fight.This conversation is a new beginning for Celie. both(prenominal) women find a moment of community, they do something together. The pronoun picuspic is finally used picI put-on. She laugh. hence us both laugh so hard us prostration down on the steppic. (Averbach). The woman who has the most profound effect on Celie is Shug Avery, Mr. ___s mistress whom he has three children with. The reader would probably think that Celie would be deeply hateful of her husbands mistress. However, she is excited to twin her because Celie feels as though she is everything that Celie could never be.Her first words to Celie though were You sure is ugly (Walker, 46 ), which is probably the most dramatically reinforced proof that Celie has ever had of her own ugliness. Celie even notices that Shug calls Mr. ____ by his real name, Albert, which demonstrates to Celie that Shug is more than just a mere servant to Mr. ____ and that Mr. deferences Shug unlike Celie. Mr. ____ goes out of his way to make Shug happy and shows her such respect. Celie doesnt understand why Shug is worthy of respect but she is not. This reiterates to Celie that Mr. ___ feels like he is superior to her but not to Shug.Shug corset with Celie and Albert for a while when she is sick and Celie takes care of her until she gets better. This is when Celie and Shug bond as woman and friends. Celie is so magnetized to Shugs independence and freedom that she loves spending this time with her. Shug is the only person, other than Nettie, who has ever treated Celie like a gentle being and enjoys her company. They share a romantic relationship later on, as well. The significance of C elie and Shugs sexual relationship is that Celie learns how to be proud of her body and that she learns how to use it to enjoy sexual intercourse.Celie has never truly enjoyed intimacy with any other person. She did it simply because she felt she had to in order to make them happy. Celie becomes Shugs only true friend. Shug is a blues singer and everyone enjoys her while she is on percentage point or sleeping with them but when she was ill none of her so called friends visited her. Celie was the only one who took care of her and spent time with her when she couldnt be the life of the party as she usually was. Shug, like Celie never had much heart and soul in her life and never knew how to love or be loved.Shug wrote Celie a song to show her appreciation for Celie and sang it to Celie at one of her concerts. This make Celie feel so good because nobody had ever showed their appreciation for anything that she had ever done. Later on in the novel Shug finds the letters that Nettie had been writing Celie for years. erstwhile Celie finds out that Mr. ___ hid all of Netties letters from her she feels anger and betrayal towards Mr. ____ because she never felt that he would do something so hurtful to her. She was still afraid(predicate) of him at this point, so she takes all the letters out of the envelopes and leaves the nvelopes, hoping that he wouldnt find out that she had found Netties letters. As she starts reading the letters she has an epiphany when she realizes that Mr. ____ tried to rape Nettie and that it was the real reason she left. She read of how Nettie was in Africa and how diverse it was compared to the small farm Celie has lived at most of her life. She finds out that her sister has been victorious care of her two children that she had with Fonso and that Fonso was not her real father. Now she feels she has something to live for and that she does not piss to be trapped by Mr. __s abuse anymore. She has a whole new family, that she thought before were dead. She wants to kill Mr. ____ for hiding all this from her but Shug tells her not to because if she did she would never be able to see her family. Celie lastly leaves town with Shug and Shugs husband, Grady, to live in Tennessee. As time goes by Celies step father passes away and Celie finds out that her real father left her his house and a dry good business. She has found a new independence by running this store. Shes excited because direct that she has a house Nettie will have a place to reelect to.Celies relationship with Shug suffers many ups and downs. Shug had moved in with Celie in her new home but left to pursue a younger man. Celie still prevails because of her newfound independence as a business woman. Shug eventually returns and lives with Celie. As Celies confidence is built she starts to understand and forgive Mr. _____. The strength of these women have with their care for one another offer opportunities for all of them to continue growing, despite the racis t and sexist world they live in.During the course of the book, they cry together, laugh together, affirm life together, and share one anothers joys. They respect one another. They live in a world that Celie could never have imagined when she was fourteen. Due to her experiences with Shug, Sofia, and Nettie, Celie is able to triumph over the sexual and racial oppression that smothered many of her female ancestors. Works Cited Walker, Alice. The Color Purple. New York Harcourt, Inc. , 2003. writings Resource Center. Averbach, Margara. 1998. Gale Group. 23 April 2007 Pifer, Lynn. Find Articles. Winter 1998. 19 April 2007 .The Color Purple

Dissent vs. Disagreement Essay

In agreement to Daniel J. Boorstins theory, superstar can rec in all several events in the history of Americas state when differment paved the path for discussions and solutions scarce dissent only produced greater separation. racket is the basis for republic because each citizen has a choice to agree or disagree and try to answer a change. For example, in the 1950s, Brown v. dining table of Education was a product of constant noise among Americans about whether sequestration of schools is constitutional or non. Because of these ongoing debates, the decision was made to stopping point segregation in schools. Similarly, a sad racial extermination in Sudan causes many arguments in the midst of the American batch as the worry worsens and Americans must decide if they should step in. Again, the inconsistency of the American state acts as its fanny for success and unity, while in Boorstins words, a democracy is kil take by strife.If in the 1950s, the African America ns chose to go on living with dissension, or deciding to forever feel apart from others, then perhaps America would not have a black president today. Because many people disagreed with the harsh racial segregation and in pairity of that time, they were able to act on their opinions and make a change that influenced the future of America. African Americans fought for equality by disagreeing, instead of dissenting, and their efforts atomic number 18 evident in todays unsegregated hostel. In Boornstins words, A person who dissents is by definition in a minority. The African Americans did not want to be known as the lesser minority, but by equal citizens of the American democracy, and the way they succeeded in make their struggles known was by debating and arguing against segregation and discrimination. Brown v. advance of Education was an egress of one of their acknowledged actions.Because of this decision, segregation in schools were finally deemed unconstitutional. An improve ment was made in the American democracy, and it was because of the life blood of democracy, which in Boorstins words, is known as Disagreement. Unlike the Brown v. Board of Education Decision, the American government loosely used dissension to deal with the race murder in Sudan. Some call it, The quiet Genocide, because at that place were many, many, casualties but there was no awareness for the issue. Although many recognized that the issue was appalling, few took action and produced debates and disagreements, do the issue to linger instead of improve. The incessant disagreement which a liberal society thrives on was overshadowed by dissension and ignorance.The genocide in Sudan was not able to be fully helped, or helped at all at first. As Boorstin says, dissension is its democracys malignant neoplastic disease and this is evident in this case because Americans chose to dissent and feel apart from this problem, which only caused it to choose worse. Boorstin recognizes the differences between dissension and disagreement in a way that makes evident that dissent is unproductive to our societys conflicts whereas disagreement serves as the first step to stretch a solution. While Brown v. Board of education is an example of how disagreement led to improvement, the issue of the genocide in Sudan showed how a great amount of dissension and a lack of discussion, disagreement and knowledge, can mo out to be a democracys cancer.

Dai Park Textbook

stochastic Manu concomitanturing &038 Service Systems Jim Dai and Hyunwoo Park School of industrial and Systems Engineering tabun Institute of applied science October 19, 2011 2 Contents 1 newsagent Problem 1. 1 Pro? t Maximization 1. 2 pull through hourimisation . 1. 3 Initial Inventory . . 1. 4 assumption . . . . . . 1. 5 operation . . . . . . . 5 5 12 15 17 19 25 25 27 29 29 31 32 33 34 39 39 40 40 42 44 46 47 48 49 51 51 51 52 54 55 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Queueing guess 2. 1 cornerst peerless . . . . . . . 2. 2 Lindley Equation . . . . 2. 3 Tra? c ardor . . . . . 2. 4 Kingman Ap masterfessionalfessionalfessional someonefessionalximation 2. 5 weenys jurisprudence . . . . . . . 2. 6 Throughput . . . . . . . 2. 7 Simulation . . . . . . . . 2. 8 course session . . . . . . . . . . . . . . . . . . . . . . . . . . . shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Discrete Time Markov cosmic string 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . 3. 1. 1 demesne Space . . . . . . . . . . . . . . . . 3. 1. 2 Transition chance Matrix . . . . . . 3. 1. 3 Initial diffusion . . . . . . . . . . . . 3. 1. 4 Markov Property . . . . . . . . . . . . . 3. 1. 5 DTMC Models . . . . . . . . . . . . . . 3. 2 unmoving dispersal . . . . . . . . . . . . . 3. 2. 1 interpreting of nonmoving Distri providedion 3. 2. 2 bureau of localiseary distri precisely whenion . . 3. 3 Irreducibility . . . . . . . . . . . . . . . . . . . 3. 3. 1 Transition Diagram . . . . . . . . . . 3. 3. 2 ap masterachability of States . . . . . . . . . . 3. 4 Periodicity . . . . . . . . . . . . . . . . . . . . . 3. 5 proceeds and Transience . . . . . . . . . . . 3. 5. 1 Geometric ergodic Variable . . . . . . 3. 6 Absorption opport structure block of measurementy . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. 7 3. 8 3. 9 3. 0 Computing Stationary Distribution Using Cut method Introduction to Binomial Stock m unrivaledtary primp Model . . . . . . Simulation . . . . . . . . . . . . . . . . . . . . . . . . . Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . limit . . . . . . . . . . . . . . . . . . . . 59 61 62 63 71 71 72 73 75 78 80 80 80 82 84 91 91 96 97 s at a clip 101 103 103 104 106 107 107 108 109 111 111 117 117 130 135 148 159 4 Poisson lick 4. 1 Exp wholearyntial Distribution . . . . . . . 4. 1. 1 Memory slight(prenominal) Property . . . . 4. 1. 2 analyse devil Exp matchlessntials 4. 2 Homogeneous Poisson Process . . . . 4. 3 Non-homogeneous Poisson Process . 4. Thinning and ruffle . . . . . . . . 4. 4. 1 Merging Poisson Process . . . 4. 4. 2 Thinning Poisson Process . . 4. 5 Simulation . . . . . . . . . . . . . . . 4. 6 Exercise . . . . . . . . . . . . . . . . 5 regular Time Markov put together up 5. 1 Introduction . . . . . . . . . . . 5. 1. 1 memory Times . . . . . 5. 1. 2 Generator Matrix . . . . 5. 2 Stationary Distribution . . . . 5. 3 M/M/1 Queue . . . . . . . . . 5. 4 Variations of M/M/1 Queue . . 5. 4. 1 M/M/1/b Queue . . . . 5. 4. 2 M/M/? Queue . . . . . 5. 4. 3 M/M/k Queue . . . . . 5. 5 capable Jackson Ne twainrk . . . . . 5. 5. 1 M/M/1 Queue look back . 5. 5. 2 Tandem Queue . . . . . 5. 5. disappointment Insp electroshock therapyion . . . 5. 6 Simulation . . . . . . . . . . . . 5. 7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Exercise declarations 6. 1 newsvendor Problem . . . . . . . 6. 2 Queueing surmise . . . . . . . . . 6. 3 Discrete Time Markov Chain . . 6. 4 Poisson Process . . . . . . . . . . 6. 5 straight Time Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Newsvendor Problem In this course, we bequeath select how to design, examine, and manage a manufacturing or military answer administration with incredulity. Our ? rst step is to understand how to light up a oneness bound last enigma lay offing uncertainty or ergodicness. 1. 1 Pro? t Maximization We ordain crop up with the simplest lawsuit interchange destructible items. figure we be kneadning a stemma marketing news composing to Georgia Tech campus. We realise to re seek a speci? c summate of copies from the publisher e actu intactlyy(prenominal) evening and sell those copies the succeeding(prenominal) guess solar twenty-four hour period.One solar twenty-four hour period, if in that location is a big news, the progeny of GT heap who necessitate to bribe and read a paper from you may be very high. An an some other(a)(prenominal)(a) day, people may except non be interested in reading a paper at all(prenominal)(prenominal). Hence, you as a retailer, provide attack the indigence variability and it is the primary uncertainty you pauperization to handle to keep your business sustainable. To do that, you motive to know what is the optimum second of copies you imp everyplaceishment to golf-club severally day. By intelligence, you know that in that respect de set astir(predicate) be a few other factors than petition you necessitate to look. Selling worth (p) How very much(prenominal) get outing you charge per paper? Buying expenditure (cv ) How muc h pull up s keeps the publisher charge per paper? This is a in aeonian court, implicateing that this woo is comparative to how legion(predicate) you effectuate. That is why it is de noned by cv . frigid commiting foothold (cf ) How much should you reconcile fair to place an commit? Ordering comprise is ? xed regardless of how legion(predicate) a(prenominal) you format. Salvage shelter (s) or safekeeping monetary value (h) in that location atomic physical body 18 deuce teddys about the remainder items. They could railway carry whatsoever monetary appraise even if expired. Otherwise, you dep permite to buy off to get righteousify of them or to storing them. If they deliver several(prenominal) value, it is portended clean value. If you hire to pay, it is called 5 6 CHAPTER 1. newsstand hustler enigma attribute contact. Hence, the future(a) relationship holds s = ? h. This is per-item value. Back swan exist (b) Whenever the actual posit is higher than how m whatever another(prenominal) a nonher(prenominal) you ready, you relapse gross changes. Loss-of-sales could address you something. You may be bookkeeping those as back browses or your brandmark may be damage. These exists volition be correspond by back lay out hold up. This is per-item woo. Your nightclub banner (y) You entrust set how many papers to be ar presentd out front you arising a day. That sum of bills is represent by y. This is your decision variable. As a business, you be get intod to want to maximise your pro? t. Expressing our pro? t as a enjoyment of these variables is the ? rst step to chance the best ordinance polity. Pro? t tole browse be interpreted in deuce ways (1) tax in get into electronegative represent, or (2) money you actualize subtraction money you pull away. allow us pad the ? rst interpretation ? rst. Revenue is represented by selling hurt (p) multiplied by how many you actually sell. Th e actual sales is bounded by the realized strike and how many you alert for the catamenia. When you order similarly many, you post sell at around as many as the number of people who want to buy. When you order similarly few, you end unless sell what you entrapd. Hence, your revenue is minimum of D and y, i. . min(D, y) or D ? y. Thinking about the bell, ? rst of all, you rush to pay something to the publisher when buying papers, i. e. cf +ycv . Two types of accessal apostrophize leave be incurred to you depending on whether your order is in a higher place or below the actual contract. When it turns out you progress tod less than the film for the period, the backorder apostrophize b per every missed sale allow occur. The fargon of missed sales send away non be negative, so it rout out be represented by max(D ? y, 0) or (D ? y)+ . When it turns out you developd much(prenominal), the total of left- all all over items overly give the sack non go negative, so it female genitalia be transported as max(y ? D, 0) or (y ? D)+ .In this way of thinking, we baffle the adjacent normal. Pro? t =Revenue ? monetary value =Revenue ? Ordering greet ? Holding approach ? Backorder live =p(D ? y) ? (cf + ycv ) ? h(y ? D)+ ? b(D ? y)+ (1. 1) How about the sulfur interpretation of pro? t? You earn p ? cv dollars every temporary hookup you sell a paper. For left-over items, you lose the outlay you bought in addition to the holding woo per paper, i. e. cv + h. When the contract is higher than what you fastend, you lose b backorder embody. Of course, you to a fault turn out to pay the ? xed ordering hail cf as well when you place an order. With this logical transcription, we boast the avocation pro? t function. Pro? t =Earning ?Loss =(p ? cv )(D ? y) ? (cv + h)(y ? D)+ ? b(D ? y)+ ? cf (1. 2) 1. 1. emolument MAXIMIZATION 7 Since we intentd devil di? erent approaches to sit the identical pro? t function, (1. 1) and (1. 2) should be equivalent. Comparing the deuce equations, you deprivation similarly notice that (D ? y) + (y ? D)+ = y. direct our quest bpetroleums down to maximizing the pro? t function. However, (1. 1) and (1. 2) contain a hit-or-miss element, the call for D. We faecal matternot maximize a function of stochastic element if we allow the ergodicness to live in our objective function. One day demand digest be very high. Another day it is to a fault mathematical nobody wants to buy a single paper. We go for to ? ure out how to get rid of this randomness from our objective function. let us denote pro? t for the nth period by gn for advertise discussion. Theorem 1. 1 (Strong Law of Large Numbers). Pr g1 + g2 + g3 + + gn = Eg1 n? n lim =1 The long- hound middling pro? t converges to the expect pro? t for a single period with probability 1. Based on Theorem 1. 1, we lowlife transfigure our objective function from just pro? t to pass judgment pro? t. In other words, by maxi mizing the anticipate pro? t, it is plightd that the long haul ordinary pro? t is maximized because of Theorem 1. 1. Theorem 1. 1 is the foundational assumption for the inherent course.When we volition talk about the long- frontier second- site something, it involves Theorem 1. 1 in about cases. Taking expectations, we detect the chase equations agree to (1. 1) and (1. 2). Eg(D, y) =pED ? y ? (cf + ycv ) ? hE(y ? D)+ ? bE(D ? y)+ =(p ? cv )ED ? y ? (cv + h)E(y ? D)+ ? bE(D ? y)+ ? cf (1. 4) (1. 3) Since (1. 3) and (1. 4) atomic number 18 equivalent, we back end choose either one of them for further discussion and (1. 4) go out be used. in the leadhand moving on, it is important for you to understand what ED? y, E(y? D)+ , E(D ? y)+ argon and how to aim them. object lesson 1. 1. picture ED ? 18, E(18 ? D)+ , E(D ? 8)+ for the demand having the quest diffusions. 1. D is a dissolved random variable. Probability mass function (pmf) is as follows. d PrD = d 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 cause For a discrete random variable, you ? rst cipher D ? 18, (18 ? D)+ , (D ? 18)+ for sepa postly of viable D values. 8 d CHAPTER 1. newsvendor trouble 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 PrD = d D ? 18 (18 ? D)+ (D ? 18)+ 10 8 0 15 3 0 18 0 2 18 0 7 18 0 12 Then, you engage the weighted middling utilise corresponding PrD = d for apiece possible D. 1 1 1 1 1 cxxv (10) + (15) + (18) + (18) + (18) = 4 8 8 4 4 8 1 1 1 1 1 19 + E(18 ?D) = (8) + (3) + (0) + (0) + (0) = 4 8 8 4 4 8 1 1 1 1 1 + E(D ? 18) = (0) + (0) + (2) + (7) + (12) = 5 4 8 8 4 4 ED ? 18 = 2. D is a unbroken random variable following resembling dispersal between 10 and 30, i. e. D ? homogeneous(10, 30). purpose Computing expectation of unbroken random variable involves integration. A consecutive random variable has probability parsimoniousness function usually denoted by f . This leave be also questful to rate the expectation. In this case, fD (x) = 1 20 , 0, if x ? 10, 30 otherwise Using this information, write in code the expectations directly by integration. ? ED ? 18 = ? 30 (x ? 18)fD (x)dx (x ? 18) 10 18 = = 10 18 1 dx 20 1 20 dx + 30 (x ? 18) x 10 dx + 18 30 (x ? 18) 1 20 dx 1 20 dx = = x2 40 1 20 + 18 x=18 x=10 18x 20 18 x=30 x=18 The key vagary is to remove the ? operator that we cannot handle by separating the integration interval into two. The other two expectations can 1. 1. cyber musculus quadriceps femoris MAXIMIZATION be figured in a similar way. 9 ? E(18 ? D)+ = ?? 30 (18 ? x)+ fD (x)dx (18 ? x)+ 10 18 = = 10 18 1 dx 20 1 20 1 20 +0 30 (18 ? x)+ (18 ? x) 10 x2 2 x=18 dx + 18 30 (18 ? x)+ 0 18 1 20 dx = dx + 1 20 dx 18x ? = 20 x=10 ? E(D ? 18)+ = ?? 30 (18 ? x)+ fD (x)dx (x ? 8)+ 10 18 = = 10 18 1 dx 20 1 20 30 (x ? 18)+ 0 10 x2 2 dx + 18 30 (x ? 18)+ 1 20 dx 1 20 dx = =0 + 1 20 dx + 18 x=30 (x ? 18) ? 18x 20 x=18 Now that we put one over registered how to rate ED? y, E(y? D)+ , E(D? y)+ , we fork over acquired the basic similarlylkit to hold the order quantity that maximizes the anticipate pro? t. premiere of all, we need to turn these expectations of the pro? t function formula (1. 4) into integration forms. For now, assume that the demand is a nonnegative day-and-night random variable. 10 CHAPTER 1. NEWSVENDOR puzzle Eg(D, y) =(p ? cv )ED ? y ? (cv + h)E(y ? D)+ ? bE(D ? y)+ ? f ? =(p ? cv ) 0 (x ? y)fD (x)dx ? ? (cv + h) 0 ? (y ? x)+ fD (x)dx ?b 0 (x ? y)+ fD (x)dx ? cf y ? =(p ? cv ) 0 xfD (x)dx + y y yfD (x)dx ? (cv + h) 0 ? (y ? x)fD (x)dx ?b y (x ? y)fD (x)dx ? cf y y =(p ? cv ) 0 xfD (x)dx + y 1 ? 0 y y fD (x)dx xfD (x)dx ? (cv + h) y 0 y fD (x)dx ? 0 y ? b ED ? 0 xfD (x)dx ? y 1 ? 0 fD (x)dx ? cf (1. 5) There can be many ways to obtain the maximum point of a function. Here we go away payoff the derived function instrument of (1. 5) and set it to zero. y that do rises the derivative equal to zero go away make Eg(D, y) either maximized or minimise depending on the ind orsement derivative.For now, assume that much(prenominal) y go away maximize Eg(D, y). We go awaying check this later. Taking the derivative of (1. 5) will involve di? erentiating an integral. allow us follow an important result from Calculus. Theorem 1. 2 (Fundamental Theorem of Calculus). For a function y H(y) = c h(x)dx, we have H (y) = h(y), where c is a constant. Theorem 1. 2 can be translated as follows for our case. y d xfD (x)dx =yfD (y) dy 0 y d fD (x)dx =fD (y) dy 0 (1. 6) (1. 7) also remember the relationship between cdf and pdf of a continuous random variable. y FD (y) = ?? fD (x)dx (1. 8) 1. 1. PROFIT MAXIMIZATION Use (1. 6), (1. 7), (1. ) to take the derivative of (1. 5). d Eg(D, y) =(p ? cv ) (yfD (y) + 1 ? FD (y) ? yfD (y)) dy ? (cv + h) (FD (y) + yfD (y) ? yfD (y)) ? b (? yfD (y) ? 1 + FD (y) + yfD (y)) =(p + b ? cv )(1 ? FD (y)) ? (cv + h)FD (y) =(p + b ? cv ) ? (p + b + h)FD (y) = 0 If we di? erentiate (1. 9) one more sentence to obtain the second derivati ve, d2 Eg(D, y) = ? (p + b + h)fD (y) dy 2 11 (1. 9) which is always nonpositive because p, b, h, fD (y) ? 0. Hence, taking the derivative and set it to zero will take us the maximum point not the minimum point. Therefore, we obtain the following result. Theorem 1. 3 ( optimum Order Quantity).The optimum order quantity y ? is the smallest y much(prenominal) that FD (y) = p + b ? cv ? 1 or y = FD p+b+h p + b ? cv p+b+h . for continuous demand D. Looking at Theorem 1. 3, it provides the following intuitions. Fixed terms cf does not a? ect the best quantity you need to order. If you can procure items for free and on that point is no holding damage, you will prepargon as many as you can. If b h, b cv , you will also prep be as many as you can. If the buying approach is almost as similar as the selling price plus backorder cost, i. e. cv ? p + b, you will prep ar nothing. You will prep ar b atomic number 18ly upon you receive an order.Example 1. 2. chew over p = 10, cf = ascorbic acid, cv = 5, h = 2, b = 3, D ? Uniform(10, 30). How many should you order for every period to maximize your long-run second-rate pro? t? come First of all, we need to compute the criterion value. p + b ? cv 10 + 3 ? 5 8 = = p+b+h 10 + 3 + 2 15 Then, we will look up the smallest y value that makes FD (y) = 8/15. 12 1 CHAPTER 1. NEWSVENDOR PROBLEM CDF 0. 5 0 0 5 10 15 20 25 30 35 40 D Therefore, we can stop that the best order quantity 8 62 = units. 15 3 Although we derived the best order quantity solution for the continuous demand case, Theorem 1. applies to the discrete demand case as well. I will ? ll in the derivation for discrete case later. y ? = 10 + 20 Example 1. 3. view p = 10, cf = 100, cv = 5, h = 2, b = 3. Now, D is a discrete random variable having the following pmf. d PrD = d 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 What is the best order quantity for every period? Answer We will use the same value 8/15 from the anterior steady-goingly pillowcase and loo k up the smallest y that makes FD (y) = 8/15. We start with y = 10. 1 4 1 1 3 FD (15) = + = 4 8 8 1 1 1 1 FD (20) = + + = 4 8 8 2 1 1 1 1 3 FD (25) = + + + = 4 8 8 4 4 ? Hence, the optimal order quantity y = 25 units.FD (10) = 8 15 8 < 15 8 < 15 8 ? 15 < 1. 2 Cost minimization depend you be a take soprano-decker of a large order in charge of operating manufacturing drags. You ar evaluate to run the factory to minimise the cost. Revenue is another persons responsibility, so all you care is the cost. To good precedent the cost of factory operation, let us set up variables in a slightly di? erent way. 1. 2. COST MINIMIZATION 13 Understock cost (cu ) It occurs when your fruit is not su? cient to meet the market demand. stock cost (co ) It occurs when you provoke more than the market demand.In this case, you may have to rent a topographic point to investment community the excess items. Unit takings cost (cv ) It is the cost you should pay whenever you be o ne unit of products. Material cost is one of this category. Fixed operating cost (cf ) It is the cost you should pay whenever you decide to start streak the factory. As in the pro? t maximation case, the formula for cost expressed in terms of cu , co , cv , cf should be develop. Given random demand D, we have the following equation. Cost =Manufacturing Cost + Cost associated with Understock Risk + Cost associated with Overstock Risk =(cf + ycv ) + cu (D ? )+ + co (y ? D)+ (1. 10) (1. 10) manifestly also contains randomness from D. We cannot pick at a random objective itself. preferably, ground on Theorem 1. 1, we will minimize evaluate cost then the long-run middling cost will be also guaranteed to be minimized. Hence, (1. 10) will be transformed into the following. ECost =(cf + ycv ) + cu E(D ? y)+ + co E(y ? D)+ ? ? =(cf + ycv ) + cu 0 ? (x ? y)+ fD (x)dx + co 0 y (y ? x)+ fD (x)dx (y ? x)fD (x)dx (1. 11) 0 =(cf + ycv ) + cu y (x ? y)fD (x)dx + co Again, we will take t he derivative of (1. 11) and set it to zero to obtain y that makes ECost minimized.We will avow the second derivative is positive in this case. Let g here denote the cost function and use Theorem 1. 2 to take the derivative of integrals. d Eg(D, y) =cv + cu (? yfD (y) ? 1 + FD (y) + yfD (y)) dy + co (FD (y) + yfD (y) ? yfD (y)) =cv + cu (FD (y) ? 1) + co FD (y) ? (1. 12) The optimal deed quantity y is obtained by setting (1. 12) to be zero. Theorem 1. 4 (Optimal Production Quantity). The optimal output quantity that minimizes the long-run fairish cost is the smallest y such that FD (y) = cu ? cv or y = F ? 1 cu + co cu ? cv cu + co . 14 CHAPTER 1. NEWSVENDOR PROBLEM Theorem 1. can be also applied to discrete demand. several(prenominal) intuitions can be obtained from Theorem 1. 4. Fixed cost (cf ) again does not a? ect the optimal doing quantity. If stock cost (cu ) is equal to unit employment cost (cv ), which makes cu ? cv = 0, then you will not maturate anything. If uni t production cost and overstock cost are negligible compared to understock cost, meaning cu cv , co , you will prepare as much as you can. To verify the second derivative of (1. 11) is indeed positive, take the derivative of (1. 12). d2 Eg(D, y) = (cu + co )fD (y) dy 2 (1. 13) (1. 13) is always nonnegative because cu , co ? . Hence, y ? obtained from Theorem 1. 4 minimizes the cost quite of maximizing it. Before moving on, let us compare criteria from Theorem 1. 3 and Theorem 1. 4. p + b ? cv p+b+h and cu ? cv cu + co Since the pro? t maximization problem solved preliminaryly and the cost minimization problem solved now share the same logic, these two criteria should be somewhat equivalent. We can see the connective by matching cu = p + b, co = h. In the pro? t maximization problem, whenever you lose a sale due to underpreparation, it costs you the opportunity cost which is the selling price of an item and the backorder cost.Hence, cu = p + b makes sense. When you overprepare, yo u should pay the holding cost for for from distributively one one left-over item, so co = h also makes sense. In sum, Theorem 1. 3 and Theorem 1. 4 are indeed the same result in di? erent forms. Example 1. 4. hazard demand follows Poisson diffusion with source 3. The cost parameters are cu = 10, cv = 5, co = 15. mark off that e? 3 ? 0. 0498. Answer The criterion value is cu ? cv 10 ? 5 = = 0. 2, cu + co 10 + 15 so we need to ? nd the smallest y such that makes FD (y) ? 0. 2. image the probability of possible demands. 30 ? 3 e = 0. 0498 0 31 PrD = 1 = e? 3 = 0. 1494 1 32 ? PrD = 2 = e = 0. 2241 2 PrD = 0 = 1. 3. INITIAL armoury Interpret these values into FD (y). FD (0) =PrD = 0 = 0. 0498 < 0. 2 FD (1) =PrD = 0 + PrD = 1 = 0. 1992 < 0. 2 FD (2) =PrD = 0 + PrD = 1 + PrD = 2 = 0. 4233 ? 0. 2 Hence, the optimal production quantity here is 2. 15 1. 3 Initial Inventory Now let us extend our warning a bit further. As debate to the assumption that we had no origin at the be ginning, suppose that we have m items when we decide how many we need to order. The solutions we have developed in previous sections assumed that we had no muniment when placing an order.If we had m items, we should order y ? ? m items instead of y ? items. In other words, the optimal order or production quantity is in fact the optimal order-up-to or production-up-to quantity. We had another unverbalized assumption that we should order, so the ? xed cost did not matter in the previous model. However, if cf is very large, meaning that starting o? a production limit or placing an order is very expensive, we may want to consider not to order. In such case, we have two scenarios to order or not to order. We will compare the pass judgment cost for the two scenarios and choose the filling with lower evaluate cost.Example 1. 5. ruminate understock cost is $10, overstock cost is $2, unit purchasing cost is $4 and ? xed ordering cost is $30. In other words, cu = 10, co = 2, cv = 4, cf = 30. occupy that D ? Uniform(10, 20) and we already possess 10 items. Should we order or not? If we should, how many items should we order? Answer First, we need to compute the optimal amount of items we need to prepare for severally day. Since cu ? cv 1 10 ? 4 = , = cu + co 10 + 2 2 the optimal order-up-to quantity y ? = 15 units. Hence, if we need to order, we should order 5 = y ? ? m = 15 ? 10 items. Let us examine whether we should actually order or not. . Scenario 1 Not To Order If we decide not to order, we will not have to pay cf and cv since we order nothing actually. We just need to consider understock and overstock risks. We will ascertain tomorrow with 10 items that we legitimately have if we decide not to order. ECost =cu E(D ? 10)+ + co E(10 ? D)+ =10(ED ? 10) + 2(0) = $50 16 CHAPTER 1. NEWSVENDOR PROBLEM Note that in this case E(10 ? D)+ = 0 because D is always greater than 10. 2. Scenario 2 To Order If we decide to order, we will order 5 items. We should pay cf and cv accordingly. Understock and overstock risks also exist in this case.Since we will order 5 items to lift up the blood line train to 15, we will run tomorrow with 15 items instead of 10 items if we decide to order. ECost =cf + (15 ? 10)cv + cu E(D ? 15)+ + co E(15 ? D)+ =30 + 20 + 10(1. 25) + 2(1. 25) = $65 Since the pass judgment cost of not ordering is lower than that of ordering, we should not order if we already have 10 items. It is overt that if we have y ? items at hands right now, we should order nothing since we already possess the optimal amount of items for tomorrows operation. It is also obvious that if we have nothing legitimately, we should order y ? items to prepare y ? tems for tomorrow. There should be a point between 0 and y ? where you are indi? erent between order and not ordering. Suppose you as a bus should give instruction to your assistant on when he/she should place an order and when should not. Instead of providing instructions for every pos sible topical fund direct, it is easier to give your assistant just one number that separates the decision. Let us call that number the life-sustaining take of real inventory m? . If we have more than m? items at hands, the anticipate cost of not ordering will be lower than the pass judgment cost of ordering, so we should not order.Conversely, if we have less than m? items presently, we should order. Therefore, when we have exactly m? items at hands right now, the pass judgment cost of ordering should be equal to that of not ordering. We will use this intuition to obtain m? value. The decision ferment is summarized in the following ? gure. m* faultfinding level for placing an order y* Optimal order-up-to quantity Inventory If your current inventory lies here, you should order. Order up to y*. If your current inventory lies here, you should NOT order because your inventory is over m*. 1. 4. SIMULATION 17 Example 1. 6.Given the same settings with the previous casing (cu = 10, cv = 4, co = 2, cf = 30), what is the slender level of current inventory m? that go downs whether you should order or not? Answer From the servicing of the previous example, we can realize that the critical value should be less than 10, i. e. 0 < m? < 10. Suppose we soon own m? items. Now, evaluate the judge costs of the two scenarios ordering and not ordering. 1. Scenario 1 Not Ordering ECost =cu E(D ? m? )+ + co E(m? ? D)+ =10(ED ? m? ) + 2(0) = cl ? 10m? 2. Scenario 2 Ordering In this case, we will order.Given that we will order, we will order y ? ?m? = 15 ? m? items. Therefore, we will start tomorrow with 15 items. ECost =cf + (15 ? 10)cv + cu E(D ? 15)+ + co E(15 ? D)+ =30 + 4(15 ? m? ) + 10(1. 25) + 2(1. 25) = 105 ? 4m? At m? , (1. 14) and (1. 15) should be equal. 150 ? 10m? = 105 ? 4m? ? m? = 7. 5 units (1. 15) (1. 14) The critical value is 7. 5 units. If your current inventory is below 7. 5, you should order for tomorrow. If the current inventory is above 7. 5, you should not order. 1. 4 Simulation Generate 100 random demands from Uniform(10, 30). p = 10, cf = 30, cv = 4, h = 5, b = 3 1 p + b ? v 10 + 3 ? 4 = = p + b + h 10 + 3 + 5 2 The optimal order-up-to quantity from Theorem 1. 3 is 20. We will compare the accomplishment between the policies of y = 15, 20, 25. Listing 1. 1 Continuous Uniform pick up Simulation Set up parameters p=10cf=30cv=4h=5b=3 How many random demands will be generated? n=100 Generate n random demands from the changeless distribution 18 Dmd=runif(n,min=10,max=30) CHAPTER 1. NEWSVENDOR PROBLEM Test the policy where we order 15 items for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 33. 4218 Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 44. 37095 Test the policy where we order 25 items for every period y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 32. 62382 You can see the policy with y = 20 maximizes the 100-period bonnie pro? t as promised by the guess. In fact, if n is relatively small, it is not guaranteed that we have maximized pro? t even if we run based on the optimal policy obtained from this section.The underlying assumption is that we should operate with this policy for a long clock. Then, Theorem 1. 1 guarantees that the sightly pro? t will be maximized when we use the optimal ordering policy. Discrete demand case can also be simulated. Suppose the demand has the following distribution. only when other parameters remain same. d PrD = d 10 1 4 15 1 8 20 1 4 25 1 8 30 1 4 The theoretic optimal order-up-to quantity in this case is also 20. Let us test three policies y = 15, 20, 25. Listing 1. 2 Discrete Demand Simulation Set up parameters p=10cf=30cv=4h=5b=3 How many random demands will be generated? =100 Generate n random demands from the discrete demand distribution Dmd=sample(c(10,15,20,25,30),n, supersede=TRUE,c(1/4,1/8, 1/4,1/8,1/4)) Test the policy where we order 15 items for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 19. 35 Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 31. 05 Test the policy where we order 25 items for every period 1. 5. reading y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 26. 55 19There are other distributions such as triangular, normal, Poisson or binomial distributions available in R. When you do your senior project, for example, you will ob exercise the demand for a part or a factory. You ? rst approximate the demand using these theoretically established distributions. Then, you can simulate the performance of possible operation policies. 1. 5 Exercise 1. Show that (D ? y) + (y ? D)+ = y. 2. Let D be a discrete random variable with the following pmf. d PrD = d run into (a) Emin(D, 7) (b) E(7 ? D)+ where x+ = max(x, 0). 3. Let D be a Poisson random variable with parameter 3.Find (a) Emin(D, 2) (b) E(3 ? D)+ . Note that pmf of a Poisson random variable with parameter ? is PrD = k = ? k ?? e . k 5 1 10 6 3 10 7 4 10 8 1 10 9 1 10 4. Let D be a continuous random variable and furnishly distributed between 5 and 10. Find (a) Emax(D, 8) (b) E(D ? 8)? where x? = min(x, 0). 5. Let D be an exponential function function function random variable with parameter 7. Find (a) Emax(D, 3) 20 (b) E(D ? 4)? . CHAPTER 1. NEWSVENDOR PROBLEM Note that pdf of an exponential random variable with parameter ? is fD (x) = ? e?? x for x ? 0. 6. David buys fruits and vegetables in large quantities and retails them at Davids Produce on La Vista Road.One of the more di? cult decisions is the amount of banana trees to buy. Let us make some simplifying assumptions, and assume that David corrupts bananas at one eon a calendar workweek at 10 cents per pound and retails them at 30 cents per pound during the week. Bananas that are mo re than a week old are too ripe and are exchange for 5 cents per pound. (a) Suppose the demand for the good bananas follows the same distribution as D given in Problem 2. What is the anticipate pro? t of David in a week if he buys 7 pounds of banana? (b) Now assume that the demand for the good bananas is similarly distributed between 5 and 10 like in Problem 4.What is the expected pro? t of David in a week if he buys 7 pounds of banana? (c) Find the expected pro? t if Davids demand for the good bananas follows an exponential distribution with mean 7 and if he buys 7 pounds of banana. 7. Suppose we are selling lemonade during a football game. The lemonade sells for $18 per gal but only costs $3 per gal to make. If we run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a value of $1. latch on that we believe the fans would buy 10 gallons with probability 0. 1, 11 gallons with probability 0. , 12 gallons with probability 0. 4, 13 gallons with probability 0. 2, and 14 gallons with probability 0. 1. (a) What is the mean demand? (b) If 11 gallons are prepared, what is the expected pro? t? (c) What is the best amount of lemonade to order before the game? (d) Instead, suppose that the demand was ordinarily distributed with mean kibibyte gallons and variance two hundred gallons2 . How much lemonade should be order? 8. Suppose that a bakery specializes in umber cakes. Assume the cakes retail at $20 per cake, but it takes $10 to prepare severally cake. Cakes cannot be sold after one week, and they have a negligible salvage value.It is projectd that the weekly demand for cakes is 15 cakes in 5% of the weeks, 16 cakes in 20% of the weeks, 17 cakes in 30% of the weeks, 18 cakes in 25% of the weeks, 19 cakes in 10% of the weeks, and 20 cakes in 10% of the weeks. How many cakes should the bakery prepare each week? What is the bakerys expected optimal weekly pro? t? 1. 5. model 21 9. A photographic photo graphic camera line of descent specializes in a event popular and fancy camera. Assume that these cameras exit obsolete at the end of the calendar calendar month. They guarantee that if they are out of stock, they will special-order the camera and promise voice communication the beside day.In fact, what the store does is to purchase the camera from an out of terra firma retailer and have it delivered through an express function. Thus, when the store is out of stock, they actually lose the sales price of the camera and the cargo ships charge, but they maintain their good reputation. The retail price of the camera is $600, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $25 for each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $480 each. (Assume that the order can only be made at the beginning of the month. (a) Assume that the demand has a discret e uniform distribution from 10 to 15 cameras a month (inclusive). If 12 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or pifflingage cost? What is the expected arrive cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) Assume that the demand can be approximated by a normal distribution with mean 1000 and measure aberrancy 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost? 10.Next months production at a manufacturing family will use a certain upshot for part of its production surgery. Assume that there is an ordering cost of $1,000 incurred whenever an order for the resoluteness is placed and the solvent costs $40 per liter. Due to short product life cycle, unused solvent cannot be used in following months. There will be a $10 disposal charge for each liter of solvent left over at the end of the month. If there is a shortage of solvent, the production surgery is seriously disrupted at a cost of $100 per liter short. Assume that the sign inventory level is m, where m = 0, 100, 300, d and 700 liters. a) What is the optimal ordering quantity for each case when the demand is discrete with PrD = 500 = PrD = 800 = 1/8, PrD = 600 = 1/2 and PrD = 700 = 1/4? (b) What is the optimal ordering policy for arbitrary initial inventory level m? (You need to specify the critical value m? in addition to the optimal order-up-to quantity y ? . When m ? m? , you make an order. Otherwise, do not order. ) (c) Assume optimal quantity will be ordered. What is the total expected cost when the initial inventory m = 0? What is the total expected cost when the initial inventory m = 700? 22 CHAPTER 1. NEWSVENDOR PROBLEM 11.Redo Problem 10 for the case where the demand is governed by the continuous uniform distribution varying between four hundred and 800 liters. 12. An automotive company will make one last production ru n of split for Part 947A and 947B, which are not interchangeable. These separate are no spacey used in new cars, but will be take as replacements for guarantee work in be cars. The demand during the sanction period for 947A is slightly normally distributed with mean 1,500,000 parts and standard deviation 500,000 parts, while the mean and standard deviation for 947B is 500,000 parts and 100,000 parts. (Assume that two demands are independent. Ignoring the cost of setting up for producing the part, each part costs only 10 cents to lift. However, if additional parts are needed beyond what has been spend a pennyd, they will be purchased at 90 cents per part (the same price for which the automotive company sells its parts). Parts remain at the end of the warrantee period have a salvage value of 8 cents per part. There has been a proposal of marriage to relieve oneself Part 947C, which can be used to replace either of the other two parts. The unit cost of 947C jumps from 10 t o 14 cents, but all other costs remain the same. (a) Assuming 947C is not produced, how many 947A should be produced? b) Assuming 947C is not produced, how many 947B should be produced? (c) How many 947C should be produced in order to satisfy the same fraction of demand from parts produced in-house as in the ? rst two parts of this problem. (d) How much money would be saved or lost by producing 947C, but concussion the same fraction of demand in-house? (e) Is your answer to question (c), the optimal number of 947C to produce? If not, what would be the optimal number of 947C to produce? (f) Should the more expensive part 947C be produced instead of the two existing parts 947A and 947B. Why? Hint compare the expected total costs. in any case, suppose that D ? Normal(, ? 2 ). q xv 0 (x? )2 1 e? 2? 2 dx = 2?? q (x ? ) v 0 q (x? )2 1 e? 2? 2 dx 2?? + = 2 v 0 (q? )2 (x? )2 1 e? 2? 2 dx 2?? t 1 v e? 2? 2 dt + Pr0 ? D ? q 2 2?? where, in the 2nd step, we changed variable by letting t = (x ? )2 . 1. 5. practise 23 13. A warranty plane section manages the after-sale wait on for a critical part of a product. The division has an obligation to replace any damaged parts in the undermentioned 6 months. The number of damaged parts X in the bordering 6 months is assumed to be a random variable that follows the following distribution x PrX = x 100 . 1 two hundred . 2 300 . 5 400 . 2The department currently has 200 parts in stock. The department needs to decide if it should make one last production run for the part to be used for the next 6 months. To start the production run, the ? xed cost is $2000. The unit cost to produce a part is $50. During the warranty period of next 6 months, if a replacement entreat comes and the department does not have a part available in house, it has to buy a part from the spot-market at the cost of $100 per part. Any part left at the end of 6 month sells at $10. (There is no holding cost. ) Should the department make the production run? I f so, how many items should it produce? 4. A store sells a particular brand of fresh succus. By the end of the day, any unsold juice is sold at a discounted price of $2 per gallon. The store gets the juice workaday from a local producer at the cost of $5 per gallon, and it sells the juice at $10 per gallon. Assume that the daily demand for the juice is uniformly distributed between 50 gallons to 150 gallons. (a) What is the optimal number of gallons that the store should order from the distribution each day in order to maximize the expected pro? t each day? (b) If 100 gallons are ordered, what is the expected pro? t per day? 15. An auto company is to make one ? al purchase of a rare railway locomotive cover to ful? ll its warranty processs for certain car models. The current price for the locomotive engine cover is $1 per gallon. If the company runs out the oil during the warranty period, it will purchase the oil from a supply at the market price of $4 per gallon. Any leftover engine oil after the warranty period is useless, and costs $1 per gallon to get rid of. Assume the engine oil demand during the warranty is uniformly distributed (continuous distribution) between 1 one million million gallons to 2 million gallons, and that the company currently has half million gallons of engine oil in stock (free of charge). a) What is the optimal amount of engine oil the company should purchase now in order to minimize the total expected cost? (b) If 1 million gallons are purchased now, what is the total expected cost? 24 CHAPTER 1. NEWSVENDOR PROBLEM 16. A company is oblilogic gated to provide warranty inspection and repair for Product A to its nodes next year. The warranty demand for the product follows the following distribution. d PrD = d 100 . 2 200 . 4 300 . 3 400 . 1 The company needs to make one production run to satisfy the warranty demand for complete next year. for each one unit costs $100 to produce the penalty cost of a unit is $500.By the end of the year, the savage value of each unit is $50. (a) Suppose that the company has currently 0 units. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. (b) Suppose that the company has currently 100 units at no cost and there is $20000 ? xed cost to start the production run. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. 17. Suppose you are course a restaurant having only one menu, lettuce salad, in the Tech Square.You should order lettuce every day 10pm after closing. Then, your supplier delivers the ordered amount of lettuce 5am next morning. origin hours is from 11am to 9pm every day. The demand for the lettuce salad for a day (11am-9pm) has the following distribution. d PrD = d 20 1/6 25 1/3 30 1/3 35 1/6 One lettuce salad requires two units of lettuce. The selling price of lettuce salad is $6, the buying price of one unit of lettuce is $1. Of course, leftover lettuce of a day cannot be used for future salad and you have to pay 50 cents per unit of lettuce for disposal. (a) What is the optimal order-up-to quantity of lettuce for a day? b) If you ordered 50 units of lettuce today, what is the expected pro? t of tomorrow? Include the purchasing cost of 50 units of lettuce in your calculation. Chapter 2 Queueing Theory Before getting into Discrete- meter Markov Chains, we will learn about universal issues in the line uping theory. Queueing theory deals with a set of frames having postponement space. It is a very powerful tool that can model a broad range of issues. Starting from analyzing a simple dress, a set of finds connected with each other will be covered as well in the end. This chapter will give you the background knowledge when you read the ask book, The end.We will revisit the finding theory once we have more advanced modeling techniques and knowledge. 2. 1 Introduction Think about a pro ceeds establishment. All of you must(prenominal) have experienced resideing in a dish musical arrangement. One example would be the Student C project or some restaurants. This is a benignant administration. A bit more automatize gain placement that has a stand up would be a call center and automated answering machines. We can imagine a manufacturing governing body instead of a military dish arrangement. These delay trunks can be reason out as a set of bu? ers and servers. There are key factors when you try to model such a system.What would you need to analyze your system? How frequently nodes come to your system? Inter- reach Times How fast your servers can serve the nodes? Service Times How many servers do you have? Number of Servers How large is your wait space? Queue Size If you can collect data about these metrics, you can characterize your queueing system. In general, a queueing system can be denoted as follows. G/G/s/k 25 26 CHAPTER 2. QUEUEING th eory The ? rst letter characterizes the distribution of inter- reach quantify. The second letter characterizes the distribution of service periods.The third number denotes the number of servers of your queueing system. The quaternary number denotes the total mental ability of your system. The 4th number can be omitted and in such case it promoter that your capacity is in? nite, i. e. your system can contain any number of people in it up to in? nity. The letter G represents a general distribution. Other prospect characters for this position is M and D and the meanings are as follows. G General Distribution M Exponential Distribution D Deterministic Distribution (or constant) The number of servers can vary from one to many to in? nity.The size of bu? er can also be either ? nite or in? nite. To simplify the model, assume that there is only a single server and we have in? nite bu? er. By in? nite bu? er, it means that space is so spacious that it is as if the limit does not e xist. Now we set up the model for our queueing system. In terms of analysis, what are we interested in? What would be the performance measures of such systems that you as a manager should know? How long should your guest wait in line on clean? How long is the postponement line on mediocre? There are two concepts of sightly. One is average over snip.This applies to the average number of guests in the system or in the queue. The other is average over people. This applies to the average hold clock age per guest. You should be able to distinguish these two. Example 2. 1. Assume that the system is empty at t = 0. Assume that u1 = 1, u2 = 3, u3 = 2, u4 = 3, v1 = 4, v2 = 2, v3 = 1, v4 = 2. (ui is ith nodes inter- reaching date and vi is ith guests service judgment of conviction. ) 1. What is the average number of customers in the system during the ? rst 10 proceedings? 2. What is the average queue size during the ? rst 10 refineds? 3.What is the average waiting time per customer for the ? rst 4 customers? Answer 1. If we call in the number of people in the system at time t with obeisance to t, it will be as follows. 2. 2. LINDLEY EQUATION 3 2 1 0 27 Z(t) 0 1 2 3 4 5 6 7 8 9 10 t EZ(t)t? 0,10 = 1 10 10 Z(t)dt = 0 1 (10) = 1 10 2. If we upchuck the number of people in the queue at time t with respect to t, it will be as follows. 3 2 1 0 Q(t) 0 1 2 3 4 5 6 7 8 9 10 t EQ(t)t? 0,10 = 1 10 10 Q(t)dt = 0 1 (2) = 0. 2 10 3. We ? rst need to compute waiting time for each of 4 customers. Since the ? rst customer does not wait, w1 = 0.Since the second customer arrives at time 4, while the ? rst customers service ends at time 5. So, the second customer has to wait 1 narrow, w2 = 1. Using the similar logic, w3 = 1, w4 = 0. EW = 0+1+1+0 = 0. 5 min 4 2. 2 Lindley Equation From the previous example, we now should be able to compute each customers waiting time given ui , vi . It requires too much e? ort if we have to draw graphs every time we need to compute wi . Let us generalize the logic behind calculating waiting clock for each customer. Let us determine (i + 1)th customers waiting 28 CHAPTER 2. QUEUEING THEORY time.If (i + 1)th customer arrives after all the time ith customer waited and got served, (i + 1)th customer does not have to wait. Its waiting time is 0. Otherwise, it has to wait wi + vi ? ui+1 . work up 2. 1, and run into 2. 2 explain the two cases. ui+1 wi vi wi+1 Time i th stretch i th service start (i+1)th arrival i th service end go into 2. 1 (i + 1)th arrival before ith service completion. (i + 1)th waiting time is wi + vi ? ui+1 . ui+1 wi vi Time i th arrival i th service start i th service end (i+1)th arrival Figure 2. 2 (i + 1)th arrival after ith service completion. (i + 1)th waiting time is 0.Simply put, wi+1 = (wi + vi ? ui+1 )+ . This is called the Lindley Equation. Example 2. 2. Given the following inter-arrival clock and service multiplication of ? rst 10 customers, compute waiting quantify and system times (time spent in the system including waiting time and service time) for each customer. ui = 3, 2, 5, 1, 2, 4, 1, 5, 3, 2 vi = 4, 3, 2, 5, 2, 2, 1, 4, 2, 3 Answer Note that system time can be obtained by adding waiting time and service time. Denote the system time of ith customer by zi . ui vi wi zi 3 4 0 4 2 3 2 5 5 2 0 2 1 5 1 6 2 2 4 6 4 2 2 4 1 1 3 4 5 4 0 4 3 2 1 3 2 3 1 4 2. 3. profession INTENSITY 9 2. 3 Suppose Tra? c Intensity Eui =mean inter-arrival time = 2 min Evi =mean service time = 4 min. Is this queueing system stalls? By stable, it means that the queue size should not go to the in? nity. Intuitively, this queueing system will not last because average service time is greater than average inter-arrival time so your system will soon explode. What was the logic behind this psyche? It was basically comparing the average inter-arrival time and the average service time. To simplify the judgement, we come up with a new quantity called the tra? c eagerness. De? ni tion 2. 1 (Tra? Intensity). Tra? c brashness ? is de? ned to be ? = 1/Eui ? = 1/Evi where ? is the arrival rate and is the service rate. Given a tra? c effectiveness, it will fall into one of the following three categories. If ? < 1, the system is stable. If ? = 1, the system is unstable unless both inter-arrival times and service times are deterministic (constant). If ? > 1, the system is unstable. Then, why dont we call ? workout instead of tra? c intensity? Utilization seems to be more visceral and user-friendly name. In fact, utilization just happens to be same as ? if ? < 1.However, the problem arises if ? > 1 because utilization cannot go over 100%. Utilization is bounded above by 1 and that is why tra? c intensity is regarded more general line to compare arrival and service rates. De? nition 2. 2 (Utilization). Utilization is de? ned as follows. Utilization = ? , 1, if ? < 1 if ? ? 1 Utilization can also be interpreted as the long-run fraction of time the server is utilized. 2. 4 Kingman Approximation Formula Theorem 2. 1 (Kingmans High-tra? c Approximation Formula). Assume the tra? c intensity ? < 1 and ? is close to 1. The long-run average waiting time in 0 a queue EW ? Evi CHAPTER 2. QUEUEING THEORY ? 1?? c2 + c2 a s 2 where c2 , c2 are square up coe? cient of transformation of inter-arrival times and service a s times de? ned as follows. c2 = a Varu1 (Eu1 ) 2, c2 = s Varv1 (Ev1 ) 2 Example 2. 3. 1. Suppose inter-arrival time follows an exponential distribution with mean time 3 transactions and service time follows an exponential distribution with mean time 2 minutes. What is the expected waiting time per customer? 2. Suppose inter-arrival time is constant 3 minutes and service time is also constant 2 minutes. What is the expected waiting time per customer?Answer 1. Tra? c intensity is ? = 1/Eui 1/3 2 ? = = = . 1/Evi 1/2 3 Since both inter-arrival times and service times are exponentially distributed, Eui = 3, Varui = 32 = 9, Evi = 2, Varvi = 22 = 4. Therefore, c2 = Varui /(Eui )2 = 1, c2 = 1. Hence, s a EW =Evi =2 ? c2 + c2 s a 1?? 2 2/3 1+1 = 4 minutes. 1/3 2 2. Tra? c intensity remains same, 2/3. However, since both inter-arrival times and service times are constant, their variances are 0. Thus, c2 = a c2 = 0. s EW = 2 2/3 1/3 0+0 2 = 0 minutes It means that none of the customers will wait upon their arrival.As shown in the previous example, when the distributions for both interarrival times and service times are exponential, the squared coe? cient of variation term becomes 1 from the Kingmans musical theme formula and the formula 2. 5. LITTLES rightfulness 31 becomes exact to compute the average waiting time per customer for M/M/1 queue. EW =Evi ? 1?? Also note that if inter-arrival time or service time distribution is deterministic, c2 or c2 becomes 0. a s Example 2. 4. You are running a highway collecting money at the entering toll gate. You reduced the utilization level of the highway from 90% to 80% by adopting car pussycat lane.How much does the average waiting time in front of the toll gate decrease? Answer 0. 8 0. 9 = 9, =4 1 ? 0. 9 1 ? 0. 8 The average waiting time in in front of the toll gate is reduced by more than a half. The Goal is about identifying bottlenecks in a plant. When you become a manager of a company and are running a expensive machine, you usually want to run it all the time with sufficient utilization. However, the implication of Kingman formula tells you that as your utilization approaches to 100%, the waiting time will be skyrocketing. It means that if there is any uncertainty or random ? ctuation foreplay to your system, your system will greatly su? er. In lower ? region, increasing ? is not that bad. If ? confining 1, increasing utilization a brusk bit can lead to a disaster. Atlanta, 10 years ago, did not su? er that much of tra? c problem. As its tra? c infrastructure capacity is getting appressed to the demand, it is ge tting more and more svelte to uncertainty. A lot of strategies presented in The Goal is in fact to decrease ?. You can do various things to reduce ? of your system by outsourcing some process, etc. You can also strategically manage or balance the load on di? erent parts of your system.You may want to utilize customer service organization 95% of time, while utilization of sales people is 10%. 2. 5 bittys Law L = ? W The Littles Law is much more general than G/G/1 queue. It can be applied to any moody box with de? nite boundary. The Georgia Tech campus can be one black box. ISyE building itself can be another. In G/G/1 queue, we can easy get average size of queue or service time or time in system as we di? erently draw box onto the queueing system. The following example shows that Littles law can be applied in broader context than the queueing theory. 32 CHAPTER 2. QUEUEING THEORY Example 2. 5 (Merge of I-75 and I-85).Atlanta is the place where two interstate highways, I-75 and I -85, merge and cross each other. As a tra? c manager of Atlanta, you would like to estimate the average time it takes to drive from the northern con? uence point to the south con? uence point. On average, 100 cars per minute enter the merged ambit from I-75 and 200 cars per minute enter the same area from I-85. You also dispatched a chopper to take a aerial snapshot of the merged area and counted how many cars are in the area. It sour out that on average 3000 cars are within the merged area. What is the average time between entering and exiting the area per fomite?Answer L =3000 cars ? =100 + 200 = 300 cars/min 3000 L = 10 minutes ? W = = ? 300 2. 6 Throughput Another focus of The Goal is set on the throughput of a system. Throughput is de? ned as follows. De? nition 2. 3 (Throughput). Throughput is the rate of output ? ow from a system. If ? ? 1, throughput= ?. If ? > 1, throughput= . The bounding bashfulness of throughput is either arrival rate or service rate depending on t he tra? c intensity. Example 2. 6 (Tandem queue with two stations). Suppose your factory production line has two stations linked in series. Every raw temporal orgasm into your line should be svelte by Station A ? rst.in one case it is processed by Station A, it goes to Station B for ? nishing. Suppose raw material is coming into your line at 15 units per minute. Station A can process 20 units per minute and Station B can process 25 units per minute. 1. What is the throughput of the entire system? 2. If we double the arrival rate of raw material from 15 to 30 units per minute, what is the throughput of the livelong system? Answer 1. First, obtain the tra? c intensity for Station A. ?A = ? 15 = = 0. 75 A 20 Since ? A < 1, the throughput of Station A is ? = 15 units per minute. Since Station A and Station B is linked in series, the throughput of Station . 7. SIMULATION A becomes the arrival rate for Station B. ?B = ? 15 = = 0. 6 B 25 33 Also, ? B < 1, the throughput of Station B is ? = 15 units per minute. Since Station B is the ? nal stage of the entire system, the throughput of the entire system is also ? = 15 units per minute. 2. Repeat the same steps. ?A = 30 ? = = 1. 5 A 20 Since ? A > 1, the throughput of Station A is A = 20 units per minute, which in turn becomes the arrival rate for Station B. ?B = A 20 = 0. 8 = B 25 ?B < 1, so the throughput of Station B is A = 20 units per minute, which in turn is the throughput of the whole system. 2. 7 SimulationListing 2. 1 Simulation of a Simple Queue and Lindley Equation N = 100 Function for Lindley Equation lindley = function(u,v) for (i in 1length(u)) if(i==1) w = 0 else w = append(w, max(wi-1+vi-1-ui, 0)) return(w) u v CASE 1 Discrete Distribution Generate N inter-arrival times and service times = sample(c(2,3,4),N,replace=TRUE,c(1/3,1/3,1/3)) = sample(c(1,2,3),N,replace=TRUE,c(1/3,1/3,1/3)) Compute waiting time for each customer w = lindley(u,v) w CASE 2 Deterministic Distribution All int er-arrival times are 3 minutes and all service times are 2 minutes Observe that nobody waits in this case. 4 u = rep(3, 100) v = rep(2, 100) w = lindley(u,v) w CHAPTER 2. QUEUEING THEORY The Kingmans theme formula is exact when inter-arrival times and service times follow iid exponential distribution. EW = 1 ? 1?? We can con? rm this equation by simulating an M/M/1 queue. Listing 2. 2 Kingman Approximation lambda = arrival rate, mu = service rate N = myriad lambda = 1/10 mu = 1/7 Generate N inter-arrival times and service times from exponential distribution u = rexp(N,rate=lambda) v = rexp(N,rate=mu) Compute the average waiting time of each customer w = lindley(u,v) mean(w) > 16. 0720 Compare with Kingman approximation rho = lambda/mu (1/mu)*(rho/(1-rho)) > 16. 33333 The Kingmans approximation formula becomes more and more straight as N grows. 2. 8 Exercise 1. Let Y be a random variable with p. d. f. ce? 3s for s ? 0, where c is a constant. (a) Determine c. (b) What is t he mean, variance, and squared coe? cient of variation of Y where the squared coe? cient of variation of Y is de? ned to be VarY /(EY 2 )? 2. Consider a single server queue. Initially, there is no customer in the system.Suppose that the inter-arrival times of the ? rst 15 customers are 2, 5, 7, 3, 1, 4, 9, 3, 10, 8, 3, 2, 16, 1, 8 2. 8. EXERCISE 35 In other words, the ? rst customer will arrive at t = 2 minutes, and the second will arrive at t = 2 + 5 minutes, and so on. Also, suppose that the service time of the ? rst 15 customers are 1, 4, 2, 8, 3, 7, 5, 2, 6, 11, 9, 2, 1, 7, 6 (a) Compute the average waiting time (the time customer spend in bu? er) of the ? rst 10 go customers. (b) Compute the average system time (waiting time plus service time) of the ? st 10 departed customers. (c) Compute the average queue size during the ? rst 20 minutes. (d) Compute the average server utilization during the ? rst 20 minutes. (e) Does the Littles law of hold for the average queue size in the ? rst 20 minutes? 3. We want to decide whether to engagement a human operator or buy a machine to key fruit steel beams with a rust inhibitor. blade beams are produced at a constant rate of one every 14 minutes. A skilled human operator takes an average time of 700 seconds to paint a steel beam, with a standard deviation of 300 seconds.An automatic painter takes on average 40 seconds more than the human painter to paint a beam, but with a standard deviation of only 150 seconds. Estimate the expected waiting time in queue of a steel beam for each of the operators, as well as the expected number of steel beams waiting in queue in each of the two cases. discover on the e? ect of variability in service time. 4. The arrival rate of customers to an ATM machine is 30 per hour with exponentially distirbuted in- terarrival times. The exertion times of two customers are independent and identically distributed.Each transaction time (in minutes) is distributed according to the following pd f f (s) = where ? = 2/3. (a) What is the average waiting for each customer? (b) What is the average number of customers waiting in line? (c) What is the average number of customers at the site? 5. A production line has two machines, machine A and tool B, that are arranged in series. Each job needs to processed by automobile A ? rst. Once it ? nishes the processing by railway car A, it moves to the next station, to be processed by Machine B. Once it ? nishes the processing by Machine B, it leaves the production line.Each machine can process one job at a time. An arriving job that ? nds the machine busy waits in a bu? er. 4? 2 se? 2? s , 0, if s ? 0 otherwise 36 CHAPTER 2. QUEUEING THEORY (The bu? er sizes are assumed to be in? nite. ) The processing times for Machine A are iid having exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the inter-arrival times of jobs arriving at the production line are iid, havi ng exponential distribution with mean of 5 minutes. (a) What is the utilization of Machine A?What is the utilization of Machine B? (b) What is the throughput of the production system? (Throughput is de? ned to be the rate of ? nal output ? ow, i. e. how many items will exit the system in a unit time. ) (c) What is the average waiting time at Machine A, excluding the service time? (d) It is know the average time in the entire production line is 30 minutes per job. What is the long-run average number of jobs in the entire production line? (e) Suppose that the mean inter-arrival time is changed to 1 minute. What are the utilizations for Machine A and Machine B, singly?What is the throughput of the production system? 6. An auto bang shop has roughly 10 cars arriving per week for repairs. A car waits outdoor(a) until it is brought inner for bumping. After bumping, the car is painted. On the average, there are 15 cars waiting outside in the yard to be repaired, 10 cars inside in the b ump area, and 5 cars inside in the painting area. What is the average length of time a car is in the yard, in the bump area, and in the painting area? What is the average length of time from when a car arrives until it leaves? 7. A small patois is sta? d by a single server. It has been observed that, during a normal business day, the inter-arrival times of customers to the bank are iid having exponential distribution with mean 3 minutes. Also, the the processing times of customers are iid having the following distribution (in minutes) x PrX = x 1 1/4 2 1/2 3 1/4 An arrival ? nding the server busy joins the queue. The waiting space is in? nite. (a) What is the long-run fraction of time that the server is busy? (b) What the the long-run average waiting time of each customer in the queue, excluding the processing time? c) What is average number of customers in the bank, those in queue plus those in service? 2. 8. EXERCISE (d) What is the throughput of the bank? 37 (e) If the inter-arr ival times have mean 1 minute. What is the throughput of the bank? 8. You are the manager at the Student affectionateness in charge of running the viands court. The food court is composed of two parts cooking station and fractures desk. Every person should go to the cooking station, place an order, wait there and pick up ? rst. Then, the person goes to the sunders desk to check out. After checking out, the person leaves the food court.The coo