1. Ken and Larry, Inc., supplies its ice cream parlors with three flavors of ice cream: chocolate, vanilla, and banana. Due to extremely hot weather and a high demand for its products, the company has run short of its supply of ingredients: milk, sugar, and cream. Hence, they will not be able to fill all the current orders received from their retail outlets, the ice cream parlors. Due to these circumstances, the company has decided to choose the amount of each flavor to produce that will maximize total profit, given the constraints on the supply of the basic ingredients.

The chocolate, vanilla, and banana flavors generate, respectively, $1.00, $0.90, and $0.95 of profit per gallon sold. The company has only 200 gallons of milk, 150 pounds of sugar, and 60 gallons of cream left in its inventory. The linear programming formulation for this problem is shown below in algebraic form. C = Gallons of chocolate ice cream produced

V= Gallons of vanilla ice cream produced

B= Gallons of banana ice cream produced

Max profit = 1.00C+0.90+0.95B

S.T.

MILK: 0.45C + 0.0.50 V +0.40B

CREAM: 0.10C+0.15V+0.20B

C>=0 V>= 0 B>=0

This problem was solved using Solver. The spreadsheet (already solved) and the sensitivity report are shown below. (Note: The numbers in the sensitivity report for the milk constraint are missing on purpose, since you will be asked to fill in these numbers in part f.)

For each of the following parts, answer the question as specifically and completely as possible without solving the problem again with Solver. Note: Each part is independent (i.e., any change made to the model in one part does not apply to any other parts).

1. What is the optimal solution and total profit?
2. Suppose the profit per gallon of banana changes to $1.00. Will the optimal solution change and what can be said about the effect on total profit?

\fD E F G LImir I'mfr MILK 1 45 1.401 T Cream 01 Chooclan Failla Toral Profe Ciallme Practiced Variable Cells Final Reduced Objective Allowable Allowable Call NanIA VAILA Cost Increase DACreAGA 18610 Gallons Produced Chocolate -0.0870 0.0375 1E + 30 Gallons Produced Vanity 0 05 0 0125 Constraints Final Shadow Constraint Allowable Allowable Call Name Value Price R. H. SIJA Increase DACIARSA 4645 Sugar Used 150 1.875 150 30 FE17 Cream Used GO 1 3.76