Question #2 A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping space for a maximum of 26 acres' worth of strawberries and 37 acres' worth of tomatoes. An acre of strawberries requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labor and 20 tons of fertilizer. The profit from an acre of strawberries is $400, and the profit from an acre of tomatoes is $300. The farmer wants to know the number of acres of strawberries and tomatoes to plant to maximize profit.

a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis. c. If the amount of fertilizer required for each acre of strawberries were determined to be 20 tons instead of 8 tons, what would be the effect on the optimal solution?

Question #4 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 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 (350degrees) but for different times40 minutes for a cake, 25 minutes for cupcakes, and 8minutes for cookiesso 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 2eggs, 0.5 cups of butter, 1.5 cups of flour, and 1 cup of sugar. A batch of 12 cupcakes requires 2eggs, 0.5cups of butter, 1.5 cups of flour, and 1 cup of sugar; and the recipe for a batch of 60cookies calls for 2 eggs, 1 cup of butter, 2 cups of flour, and 1 cup of sugar. Alocal 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 to maximize the money they make. a. Formulate a linear programming model for this problem. b. Solve this model using the computer. excel c. If the members can get more of a resource, which should it be, and how much? Explain your answer.

Question #5 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 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 (350degrees) but for different times40 minutes for a cake, 25 minutes for cupcakes, and 8minutes for cookiesso 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 2eggs, 0.5 cups of butter, 1.5 cups of flour, and 1 cup of sugar. A batch of 12 cupcakes requires 2eggs, 0.5cups of butter, 1.5 cups of flour, and 1 cup of sugar; and the recipe for a batch of 60cookies calls for 2 eggs, 1 cup of butter, 2 cups of flour, and 1 cup of sugar. Alocal 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 to maximize the money they make. a. Formulate a linear programming model for this problem. b. Solve this model using the computer. excel c. If the members can get more of a resource, which should it be, and how much? Explain your answer.