Reference no: EM132574492

Bainouna company in Dubai produces 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 supply of the basic ingredients.

The chocolate, vanilla, and banana flavors generate, respectively, 45 AED, 34 AED, and 40 AED of profit per gallon sold. The company has only 220 gallons of milk, 160 pounds of sugar, and 80 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 vanilla ice cream produced,

B = gallons of banana ice cream produced.

Maximize Profit = 45 C + 34 V + 40 B,

subject to

Milk: 0.45 C + 0.50 V + 0.40 B ≤ 220 gallons

Sugar: 0.50 C + 0.40 V + 0.40 B ≤ 160 pounds

Cream: 0.10 C + 0.15 V + 0.20 B ≤ 80 gallons

and

C ≥ 0, V ≥ 0, B ≥ 0.

Question 1. What is the optimal solution?

Question 2. What is the optimal total profit?

Question 3. What is the impact of one additional gallon of milk (1st ressource)? Explain.

Question 4. Suppose the company has the opportunity to buy an additional 9 pounds of sugar (2nd ressource) at a total cost of 350AED. Should they? Explain.

Question 5. Suppose the company discovers that 4 gallons of cream (3rd ressource) 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?

Question 6. Suppose that for maintenance reasons, an additional (technical) constraint stipulates that the total number of gallons produced (C + V + B) is less than 410. Does optimal total profit change?