It had been a dream come 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 piece1 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- generateddrawing 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 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.

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 theexhibit.

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 Lyman as from Rick Rawls 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 display 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 population 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?, Beyond, 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.

1. 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?

Artist Piece Description of Piece Price Colin Zweibell Perfection A wire-mesh sculpture of the human body $300,000 Burden A wire-mesh sculpture of a mule 250,000 The Great Equalizer A wire-mesh sculpture of a gun 125,000 Rita Losky Chaos Reigns A series of computer-generated drawings 400,000 Who Has Control? A computer-generated drawing intermeshed with lines of computer code 500,000 Domestication A pen-and-ink drawing of a house 400,000 Innocence A pen-and-ink drawing of a child 550,000 Norm Marson Aging Earth A sculpture of trash covering a larger globe 700,000 Wasted Resources A collage of various packaging materials 575,000 Candy Tate Serenity An all-blue watercolor painting 200,000 Calm before the A painting with an all-blue watercolor background and a 225,000 Storm black watercolor center Robert Bayer Void An all-black oil painting 150,000 Sun An all-yellow oil painting 150,000 David Lyman Storefront Window A photo-realistic painting of a jewelry store display window 850,000 Harley 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) Trojan Victory A wooden sculpture of a condom Rick Rawls Rick Rick II Rick III 175,000 450,000 500,000 500,000 500,000 Bill Reynolds Beyond 650,000 Pioneers Bear Canton Wisdom An oil painting of three astronauts aboard the space shuttle A pen-and-ink drawing of an Apache chieftain 650,000 250,000 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 Helen Row Study of a Violin A cubist painting of a violin Study of a Fruit Bowl A cubist painting of a bowl of fruit 450,000 400,000 400,000 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 50,000* Winding Road A watercolor painting of Lombard Street 50,000* Dreams Come True A watercolor painting of the San Francisco Museum of Modern Art 50,000* A photo-realistic self-portrait (painting) A cubist self-portrait (painting) An expressionist self-portrait (painting) A science fiction oil painting depicting Mars colonization