An ice cream parlor wants to make three different types of ice cream: Vanilla,Strawberry, and Peach-cherry. The parlor has 120 cups of cream, 48 eggs, and 32 cups of sugar on hand. The vanilla ice cream recipe calls for 4 cups of cream, 1 egg, and 0.75 cup of sugar. The strawberry ice cream recipe calls for 2 cups of cream, 2 eggs, and 0.75 cup of sugar. The peach-cherry ice cream recipe calls for 4 cups of cream, 1 egg, and 1.25 cups of sugar. Each recipe yields 1.5 quarts of ice cream. The parlor needs at least 18 quarts of vanilla and at least 6 quarts of each of the other varieties. The parlor wants to maximize the amount of ice cream produced. How many batches of each variety of ice cream does the parlor need to produce?

a) Formulate the linear programming problem that needs to be solved to maximize the amount of ice cream produced. (Hint: Let x be the number of times that vanilla ice-cream recipe is used and define y and z similarly).

b) By using Excels Solver solve the above optimization problem. To get credit you must clearly indicate value of each variable for the optimal solution along with maximum amount of ice cream produced.

Below is an example of how we should solve the excel part. Please solve it in this way. (Like replace the values in the below table and follow its format)

Variables Values Coefficients 0 0 0 3 Profit 0 Constraint 1 X 2 0 -5 1 1 2 4 z 1 3 Value Limit 0 130 310 0 30 0 100 s/sle 130 -310 -30 -100 3 2 0 1 1 Variables Values Coefficients 0 0 0 3 Profit 0 Constraint 1 X 2 0 -5 1 1 2 4 z 1 3 Value Limit 0 130 310 0 30 0 100 s/sle 130 -310 -30 -100 3 2 0 1 1