Business, 25.03.2021 22:20 michibabiee

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 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.
Let

C=Gallons of chocolate ice cream produced
V=Gallons of vanillaice cream produced
B=Gallons of banana ice cream produced
Maximize Profit= 1.00C+0.90V+0.95B

subject to

Milk:0.45C + 0.50V + 0.40B ≤ 200gallons
Sugar:0.50C + 0.40V + 0.40B ≤ 150pounds
Cream:0.10C + 0.15V + 0.20B ≤ 60gallons
and

C ≥ 0 V ≥ 0 B ≥ 0

Required:
a. What is the optimal solution and total profit?
b. 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?
c. Suppose the profit per gallon of banana changes to 92¢. Will the optimal solution change and what can be said about the effect on total profit?
d. Suppose the company discovers that three gallons of cream have gone sour and so must be thrown out. Will the optimal solution change and what can be said about the effect on total profit?

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