- 274 Chapter Seven Using Binary Integer Programming To Deal With Yes Or No Decisions Harley Beyond Artist Piece Descripti 1 (297.04 KiB) Viewed 22 times
274 Chapter Seven Using Binary Integer Programming to Deal with Yes-or-No Decisions Harley Beyond Artist Piece Description of Piece Price David Lyman Storefront Window A photo-realistic painting of a jewelry store display window 850.000 A photo-realistic painting of a Harley-Davidson motorcycle 750,000 Angie Oldman Consumerism A collage of magazine advertisements 400,000 Reflection A mirror (considered a sculpture) 175.000 Trojan Victory A wooden sculpture of a condom 450.000 Rick Rawls RICK A photo-realistic self-portrait (painting) 500,000 Rick A cubist self-portrait (painting) 500.000 Rick W An expressionist self-portrait (painting) 500,000 Bill Reynolds A science fiction oil painting depicting Mars colonization 650,000 Pioneers An oil painting of three astronauts aboard the space shuttle 650,000 Bear Canton Wisdom A pen-and-ink drawing of an Apache chieftain 250.000 Superior Powers A pen-and-ink drawing of a traditional Native American rain dance 350,000 Living Land An oil painting of the Grand Canyon 450 000 Helen Row Study of a Violin A cubist painting of a violin 400.000 100 Study of a Fruit Bowl A cubist painting of a bowl of fruit 400,000 Ziggy Lite My Namesake A collage of Ziggy cartoons 300,000 Narcissism A collage of photographs of Ziggy Lite 300,000 Ash Briggs All That Glitters A watercolor painting of the Golden Gate Bridge 50.000 The Rock A watercolor painting of Alcatraz Winding Rood A watercolor painting of Lombard Street 50,000 Dreams Come True A watercolor painting of the San Francisco Museum of Modern Art 50.000 *Ash does not require personal compensation, and the cost for moving his pieces to the museum from his home in San Francisco is minimal. The cost of displaying his pieces therefore only includes the cost of constructing the display and insuring the pieces. 50,000- forms. is displayed. Furthermore, Ash wants to expose viewers to all painting styles, but he wants to limit the number of paintings displayed to achieve a balance in the exhibit between paintings and other art forms. He therefore decides to include at least one photo-realistic painting, at least one cubist painting, at least one expressionist painting, at least one watercolor painting, and at least one oil painting. At the same time, he wants the number of paintings to be no greater than twice the number of other art Ash wants all his own paintings included in the exhibit since he is sponsoring the exhibit and since his paintings celebrate the San Francisco Bay area, the home of the exhibit. Ash possesses personal biases for and against some artists, Ash is currently having a steamy affair with Candy Tate, and he wants both of her paintings displayed. Ash counts both David Lyman and Rick Rawls as his best friends, and he does not want to play favorites between these two artists. He therefore decides to display as many pieces from David Lymana from Rick Rawls Type and to display at least one piece from each of them. Although Ziggy Lite is very popular within art circles, Ash believes Ziggy makes a mockery of art. Ash will therefore only accept one dis- play piece from Ziggy, if any at all. Celeste also possesses her own agenda for the exhibit. As a museum director, she is interested in representing a diverse pop- ulation of artists, appealing to a wide audience, and creating a politically correct exhibit. To advance feminism, she decides to include at least one piece from a female artist for every two pieces included from a male artist. To advance environmentalism, she decides to include either one or both of the pieces Aging Earth and Wasted Resources. To advance Native American rights, she decides to include at least one piece by Bear Canton. To advance science, she decides to include at least one of the following pieces: Chaos Reigns, Who Has Control?, Bevond, and Pioneers. Celeste also understands that space is limited at the museum. The museum only has enough floor space for four sculptures and enough wall space for 20 paintings, collages, and drawings. Finally, Celeste decides that if Narcissism is displayed, Reflection should also be displayed since Reflection also suggests narcissism. Please explore the following questions independently except where otherwise indicated. a. Ash decides to allocate $4 million to fund the exhibit. Given the pieces available and the specific requirements from Ash and Celeste, formulate and solve a binary integer program- ming problem to maximize the number of pieces displayed in the exhibit without exceeding the budget. How many pieces are displayed? Which pieces are displayed? b. To ensure that the exhibit draws the attention of the pub- lic, Celeste decides that it must include at least 20 pieces. Formulate and solve a binary integer programming prob- lem to minimize the cost of the exhibit while displaying at least 20 pieces and meeting the requirements set by Ash and Celeste. How much does the exhibit cost? Which pieces are displayed? c. An influential patron of Rita Losky's work who chairs the museum's board of directors learns that Celeste requires at least 20 pieces in the exhibit. He offers to pay the minimum amount required on top of Ash's $4 million to ensure that exactly 20 pieces are displayed in the exhibit and that all of Rita's pieces are displayed. How much does the patron have to pay? Which pieces are displayed?