Reference no: EM132840413

The linear programming model for this problem: Maximize Z = $4.15X1 + $3.6X2

Gillian's Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons of both products. A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs $0.93, and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.15 and profit per gallon of yogurt is $3.60.

Subject to

(1) X1 + X2 <= 115

(2) 0.93X1 + 0.75X2 <= 90

(3) X1 - 2X2 >= 0

X1, X2 >= 0

a. Graph the constraint lines and mark them clearly with the numbers (1), (2) and (3) to indicate which line corresponds to which constraint. Darken the feasible region.

b. Determine the optimal solution(s) and the Maximum value of the objective function. (Show your calculation). Include "managerial statements" that communicate the results of the analyses (i.e. describe verbally the results).

c. How much additional profit would the restaurant realize each week if it increased its freezer capacity to accommodate 20 extra gallons of ice cream and yogurt? Justify.