...foIntro to Linear Programming Motivation: A baker has 150 kg flour, 22 kg sugar, and 27.5 kg of butter to make the following two type of cakes: 1 dozen of this cake needs 3 kg flour 1 kg sugar 1 kg butter 1 dozen of this cake needs 6 kg flour 0.5 kg sugar 1 kg butter Profit from 1 dozen is $20 Profit from one dozen is $30 How many dozen from each cakes should the baker make to maximize his profit? Geometric solution: Geometric solution: The contour of z with the highest function value touches the feasible set at the point B. To find the coordinates of B we intersect the flour and butter border: 3x1+6x2=150 x1+x2=27.5 and get x1=5 and x2=22.5. Hence the maximum profit is 775 dollars. x1 C x2 Ä 450 x1 x2 x1 x1 x2 0 x2 0 2x1 C 3x2 3x1 C 2x2 Ä 1200 x1 C 2x2 Ä 800 x1 C x2 Ä 450 0; x2 0: Setting upx a problem: 1 x1 x2 3;500x1 C 3;000x2 .x1 ; x2 / x1 C x2 Ä 450 x1 x2 x1 x1 0 12;000x1 C 4;000x2 x2 x2 0 12;000x1 C 4;000x2 2x1 C 3x2 3x1 C 2x2 Ä 1200 4;000x1 C 4;000x2 x1 C 2x2 Ä 800 x1 C x2 Ä 450 0; x2 1;000x1 C 5;000x2 0: x1 x1 x2 x1 32;000 20;000 x1 3;500x1 C 3;000x2 12;000x1 C 4;000x2 4;000x1 C 4;000x2 1;000x1 C 5;000x2 0; x2 0: x1 Solution: 48;000 0 x2 0 48;000 32;000 20;000 x2 3;500x1 C 3;000x2 .x1 ; x2 / 12;000x1 C 4;000x2 12;000x1 C 4;000x2 48;000 4;000x1 C 4;000x2 32;000 1;000x1 C 5;000x2 x1 ...
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...Duality It is possible to discuss a country and be able to define its culture, except when discoursing on America. America is a melting pot of nations and the individual cultures that have relocated here. Men, women, children and families have come to seek freedom from persecution or to seek opportunity that does not exist in their own country of origin. Living in America and being Black, Latino or Chinese may cause a duality of identity that makes a covenant impossible. You are told to speak English, go to college, become educated and be more than your parents were, yet you want to retain the culture of your youth. Your own family is telling you to change; it becomes a battle of soul. Your culture intertwines with the education you receive and it is problematic to distinguish who you are. Three pieces of literature show how difficult it is to deal with this duality: “A Red Sweater” by Fae Myenne Ng, “America” by Claude McKay and “Spanish Roulette” by Ed Vega. Each piece is different, each has its own voice, yet each speak of duality and the frustration it brings trying to unite one world with another, being an American and trying to maintain your cultural identity. What is life as a Latino man in America? Ed Vega writes that it is “Spanish Roulette,” the somewhat futile desire to accept the duality of living two cultures. Spanish roulette is taking the chance to live life differently, to live outside the walls, outside the culture, to make the break, face the pain, and...
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...In her article, Linh Hua analyzes the duality of Kindred’s speculative and historical fiction, breaks down Butler’s contrasting gender and race characterization, and considers its effectiveness in communicating the pro-black and pro-feminist themes of the book. Hua contends that contemporary literature necessitates a “black feminist sentimentality”: authors must dramatize depictions of the violation and mismanagement of blacks and females as a necessary byproduct of a progressive depiction of past oppression (Hua 391). Hua’s article revolves around illuminating various facets of black feminist sentimentality, textually supporting each point with comparisons of the interactions and developments between Dana and Alice and their respective male...
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...image. The story Gilgamesh, edited by Stephen Mitchell, uses duality to convey how the same person reacts to being exposed to two opposite scenarios. Gilgamesh is a telling of a lonely king with god-like powers, until one day, the gods finally make him a companion named Enkidu who is equal to him. Within this epic, there are many examples of duality, but there are three main ones which are: Gilgamesh and Enkidu themselves, Gilgamesh and Enkidu's battle against Humbaba and later the Bull of Heaven, and the contrast between Gilgamesh at the beginning of the story and at the end. In the epic, Gilgamesh has no one to rival him which causes him to do whatever he wants to his people. His suffer from his tyranny, so then they pray to the gods for help. The gods hear their cry and decide...
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...and Evil Does Exist in Man The central theme of the duality of man is demonstrated in The Robber Bridegroom by Eudora Welty. The world is comprised of contrasts such as light and dark, and just as there are characters who are motivated by greed, there are characters who are motivated by the love in their hearts. The duality of the character’s actions in The Robber Bridegroom prove that the capacity for good and evil exist within all people. Jamie is described as a bandit and a gentleman, he robs people in the woods, but he gifts people generously and eventually starts to think before he kills. When Jamie was still the bandit of the woods, he took the innocence of a girl named Rosamond, on page 65 the author tells the reader that Jamie, “Robbed her [Rosamond] of that which he had left her the day before.” His morality is shown on page 183...
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...Things are not always what they seem. Nathaniel Hawthorne's The Scarlet Letter uses the central idea of duality to exemplify this. A key symbol of duality Hawthorne presents in The Scarlet Letter is Hester Prynne's embodiment of her sin: the beautifully embroidered scarlet letter. Forcibly placed upon Hester's bosom, the letter punishes her for committing adultery with the town reverend, Arthur Dimmesdale. The badge also intends to outcast her and her daughter, Pearl, from the Puritan society of Boston. Although the "A" originally acted as Hester's punishment, the interpretation of the scarlet letter varies for Dimmesdale and Pearl to juxtapose Hester's unwavering perspective. Besides Hester Prynne, Arthur Dimmesdale has the biggest personal...
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...From this oppressed and tragic history and the struggle of adopting and refusing the European American culture, unintentionally a new culture of duality prevailed. In the start of the novel, both Nanapush and Pauline’s narrations are set on one way of life, either the Native American storytelling, deerskin cloths, and open wigwams, or the European American way of modernization, westernization, and civilization. Yet, by conclusion they both discern the partial assimilation and that a balance of both cultures is the only way the tribe will remain. This solution- or rather subconscious necessity- of cultural duality is exhibited in Nanapush, Pauline, and Fleur. Their journeys in this time of disjointed identity and threat to what is known highlights...
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...In today’s society, people often create a figure of themselves, making them act like someone they are not. They do this by creating a public face, which is used in front of other people, and a private one, which shows the person's true desires and intentions. This duality is necessary to please others around them, while still pleasing themselves. William Shakespeare’s, Julius Caesar, had the conspirators, and Julius Caesar himself construct public and private faces in front of one another, and Rome. The characters use these faces to deceive one another to please themselves, and one another, covering up their true intentions. The play begins with Julius Caesar, the soon to be leader, swaying the crowd with his roaring personality and invulnerability. When the soothsayer exclaims...
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...Two-Faced Duality refers to the concept of having two different opposing ideas act as different faces of a single entity. In Romeo and Juliet, by William Shakespeare, the characters act contrary to themselves as the plot flips entirely to a tragic standpoint. Duality is a common theme personified in Romeo and Juliet and is the pivot that makes a play that could have been a comedy a solemn tragedy. It is seen in the swings of mood of Mr. Capulet and the Friar as they move from conservative stances into quick decisions. Mr. Capulet is one of the best representations of this concept as he struggles with himself on how to make Juliet happy. The first face of Mr Capulet is seen as he delays his agreement to Paris’ proposal, stating, “My will to her consent is but a par. / And, she agreed, within her scope of choice / Lies my consent and fair...
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...Since time immemorial, mankind has created objects and methods to make their lives easier. We commonly refer to these innovations as technology. From the first wooden spear created by the caveman to the latest augmented reality of today’s Silicon Valley, these innovations have been technology. Since technology has been adopted, there have been naysayers that have always spouted the same lines of “This technology is going to ruin us” and “This technology is evil”. In this essay, we will show the duality of technology by the destructive nature of it, the beneficial nature, and the choices mankind makes when it puts these technologies into practice. In 1945, at 5:29:45 a.m., the Manhattan Project came to an explosive end as the first atom bomb...
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...There often exists an ambiguity in Poe’s work. This duality is prevalent in “Ligeia.” The reader is left with a quandary at the end of the narrative. Is the narrator experiencing some supernatural phenomenon or is the narrator unreliable due to his drug use, insanity, or any other number of reasons? Ligeia is described with specific markers early in the story giving the reader the impression that she is from a multitude of cultural areas and has lived in ancient times. Her husband claims she has the nose of Hebrews, a chin of the Greeks, and the beauty of the Turkish people (Poe 394-395). She can also speak a multitude of ancient languages. The narrator states, that “In the classical tongues was she deeply proficient” (Poe 396). These suggest, along with other intimations, that she may have...
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...Hayao Miyazaki attained global acclaim for both Princess Mononoke, released in the United States in 1999, and Spirited Away, released throughout North America three years later. These films are clearly products of the same visionary; each film presents a protagonist of strong will and sound ethic and, in each case, he or she is forced to embark on an epic journey. Both films were very successful in Japan; however, although both were critically acclaimed in the United States, only Spirited Away saw continued box-office success. In order to explain the disparity between these films’ earnings, I will discuss the different approaches, which these films take, to the theme of duality. Naturally, the idea of a double nature is unsettling. However, whereas Spirited Away addresses this theme in a way that invigorates and provides closure, Princess Mononoke leaves the audience feeling uncertain. In order to understand the disparity between these films’ earnings, one must examine not only thematic differences between these films, but also patterns among high-grossing films in the United States. In other words, what are American audiences looking for, which Spirited Away offers and Princess Mononoke does not? When reviewing the history of box-office successes in the United States, one becomes aware of an unfortunate truth: that there is little correlation between what viewers recognize as ‘good cinema’ and what they will pay to see. So what is the formula for a box office success...
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...Robert Louis Stevenson’s 1886 novel The Strange Case of Dr. Jekyll and Mr. Hyde delves deep into the topic of duality. It follows a London lawyer by the name of Gabriel John Utterson who investigates the odd circumstances surrounding his old friend, Dr. Henry Jekyll, and Jekyll’s evil counterpart, Mr. Edward Hyde. Like many other gothic novels from its time, Dr. Jekyll and Mr. Hyde shows a prevalent theme of duality, in that it centers on the polarity between good and evil. The Strange Case of Dr. Jekyll and Mr. Hyde deals with a Dr. Henry Jekyll who is widely respected, successful, and possesses a brilliant intellect but is only too aware of the duplicity of the life that he leads, and of the evil that resides within him. Dr. Jekyll covertly...
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...Duality is the idea of everything having an opposing truth. In Robert Louis Stevenson’s book, The Strange Case of Dr. Jekyll and Mr. Hyde, duality is the main theme. Stevenson explores the concept of duality with the setting, events that take place throughout the story and this character’s dialogue. William Shakespeare’s play, Romeo and Juliet, also demonstrates the inherent duality of the world. The dualities in The Strange Case of Dr. Jekyll and Mr. Hyde consist of the duality of human nature and the duality of society; Romeo and Juliet ties in with some of these dualities. Dr. Jekyll, a character in Stevenson’s novel, is used a common example of the duality in human nature. Dr. Jekyll was thought to be an entirely good person, by the Victorian...
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...Anmol Shah Mr. Stovall and Mr. Chan English 10 29 October 2015 The Duality of Dr. Jekyll & Mr. Hyde In the novella by Robert Louis Stevenson, The Strange Case of Dr. Jekyll & Mr. Hyde portrays the duality of a human. Every human being has a good and bad side. In the novella, Dr. Jekyll is represented as a dualistic person. Dr. Jekyll is a good well-mannered scientist and conducts an experiment that brings out his evil side, Mr. Hyde. This tells the reader that every man has a bad side and one can be more in control than the other. In this case Mr. Hyde beings to corrupt Dr. Jekyll and causes major damage. Does Dr. Jekyll think of Mr. Hyde of himself or as another person? Should the blame of Sir Danvers Carew be Mr. Hyde himself or Dr. Jekyll? Dr. Jekyll believes that a man cannot ever be pure good, but he cannot avoid the evil....
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