The honorary business fraternity at Tech is planning an all-day bake sale on Saturday of a home football game as a charity fund-raising project. The members will bake cakes, cupcakes, and cookies in one of the member's apartment oven starting at 5 p.m. on Friday after the members get out of class until midnight. All the items bake at the same temperature (350 degrees) but for different times-40 minutes for a cake, 25 minutes for cupcakes, and 8 minutes for cookies-so they will bake one item at a time. The oven has enough space to bake a batch of 12 cakes or 48 cupcakes or 60 cookies at a time. The recipe for a cake calls for 2 eggs, 0.5 cups of butter, 1.5 cups of flour, and 1 cup of sugar. A batch of 12 cupcakes requires 2 eggs, 0.5 cups of butter, 1.5 cups of flour, and 1 cup of sugar; and the recipe for a batch of 60 cookies calls for 2 eggs, 1 cup of butter, 2 cups of flour, and 1 cup of sugar. A local grocery store has donated 10 dozen eggs and 30 pounds each of butter, sugar, and flour. (1 pound of butter equals 2 cups, 1 pound of sugar equals 2.4 cups, and 1 pound of flour equals 4 cups). The members plan to sell cakes for $15 apiece, cupcakes for $3 apiece, and cookies for $2 apiece. The members want to know how many of each item they should bake in order to maximize the money they make.

a. Formulate a linear programming model for this problem.

b. Solve this model using the computer.

c. If the members can get more of a resource, which should it be and how much? Explain your answer.