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 programming 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 public, Celeste decides that it must include at least 20 pieces.

Formulate and solve a binary integer programming problem 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?

It had been a dream comes true for Ash Briggs, a struggling artist living in the San Francisco Bay area. He had made a trip to the corner grocery store late one Friday afternoon to buy some milk, and, on impulse, he had also purchased a California lottery ticket. One week later, he was a multimillionaire.

Ash did not want to squander his winnings on materialistic, trivial items. Instead he wanted to use his money to support his true passion: art. Ash knew all too well the difficulties of gaining recognition as an artist in this post-industrial, technological society where artistic appreciation is rare and financial support even rarer. He therefore decided to use the money to fund an exhibit of up-and-coming modern artists at the San Francisco Museum of Modern Art.

Ash approached the museum directors with his idea, and the directors became excited immediately after he informed them that he would fund the entire exhibit in addition to donating $1 million to the museum. Celeste McKenzie, a museum director, was assigned to work with Ash in planning the exhibit. The exhibit was slated to open one year from the time Ash met with the directors, and the exhibit pieces would remain on display for two months.

Ash began the project by combing the modern art community for potential artists and pieces. He presented a list (shown below) of artists, their pieces, and the price of displaying each piece 1 to Celeste.

Ash possesses certain requirements for the exhibit. He believes the majority of Americans lack adequate knowledge of art and artistic styles, and he wants the exhibit to educate Americans.

Ash wants visitors to become aware of the collage as an art form, but he believes collages require little talent. He therefore decides to include only one collage. Additionally, Ash wants viewers to compare the delicate lines in a three-dimensional wire mesh sculpture to the delicate lines in a two-dimensional computer-generated drawing. He therefore wants at least one wire-mesh sculpture displayed if a computer-generated drawing is displayed. Alternatively, he wants at least one computer generated drawing displayed if a wire-mesh sculpture 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 forms.

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.................

Transcribed Image Text:

Description of Piece Artist Piece Price Colin Zweibell Perfection Burden A wire-mesh sculpture of the human body $300,000 250,000 A wire-mesh sculpture of a gun A series of computer-generated drawings A computer-generated drawing intermeshed with lines of computer code A pen-and-ink drawing of a house A pen-and-ink drawing of a child A sculpture of trash covering a larger globe A collage of various packaging materials An all-blue watercolor painting A painting with an all-blue watercolor background and a black watercolor center An all-black oil painting An all-yellow oil painting A photo-realistic painting of a jewelry store display window A photo-realistic painting of a Harley-Davidson motorcycle A collage of magazine advertisements A mirror (considered a sculpture) A wooden sculpture of a condom A photo-realistic self-portrait (painting) A cubist self-portrait (painting) An expressionist self-portrait (painting) A science fiction oil painting depicting Mars colonization An oil painting of three astronauts aboard the space shuttle The Great Equalizer Chaos Reigns Who Has Control? 125,000 400,000 500,000 Rita Losky 400,000 550,000 700,000 575,000 200,000 225,000 Domestication Innocence Norm Marson Aging Earth Wasted Resources Serenity Calm before the Storm Candy Tate Robert Bayer Void 150,000 150,000 850,000 750,000 400,000 175,000 450,000 500,000 500,000 500,000 650,000 650,000 250,000 350,000 450,000 400,000 400,000 300,000 300,000 50,000* 50,000* 50,000* 50,000* Sun Storefront Window Harley Consumerism Reflection David Lyman Angie Oldman Trojan Victory Rick Rick I Rick IN Rick Rawis Bill Reynolds Beyond Pioneers Wisdom Superior Powers Living Land Study of a Violin Study of a Fruit Bowl My Namesake Narcissism All That Glitters The Rock Bear Canton A pen-and-ink drawing of a traditional Native American rain dance An oil painting of the Grand Canyon A cubist painting of a violin A cubist painting of a bowl of fruit A collage of Ziggy cartoons A collage of photographs of Ziggy Lite A watercolor painting of the Golden Gate Bridge A watercolor painting of Alcatraz A watercolor painting of Lombard Street A watercolor painting of the San Francisco Museum of Modern Art Helen Row Ziggy Lite Ash Briggs Winding Road Dreams Come True *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.