2 A. The production planner for a private label soft drink maker is planning the

Question

2 A. The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. Formulate this problem as a linear programing Problem. (Write down the decision variables, objective function and all constraints.) (DO NOT Solve this Problem. (10 points)

Explanation / Answer

Solution :

Let X 1 be the decision variable for case of root beer

Let X 1 be the decision variable for  sassafras soda .

In this equation the profit of root bear & sassafras soda is mentioned . So this problem is of maximization.

So LPP formulation will be

Maximization Z = 6 X1 + 4 X2

subject to

2 X1 + 3 X2 < = 12 Hours (Production Time Constraint)

5 X 1 + 5 X 2 < = 1500 Gallons (Carbonated water Constraint)

where X 1 , X 2 > = 0

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