Question

Let P1 = number of Product 1 to be produced P2 = number of Product 2...

Let P1 = number of Product 1 to be produced

P2 = number of Product 2 to be produced

P3 = number of Product 3 to be produced

P4 = number of Product 4 to be produced

Maximize 15P1 + 20P2 + 24P3 + 15P4 Total profit

Subject to

8P1 + 12P2 + 10P3 + 8P4 ≤ 3000 Material requirement constraint

4P1 + 3P2 + 2P3 + 3P4 ≤ 1000 Labor hours constraint

P2 > 120 Minimum quantity needed for Product 2 constraint

And P1, P2, P3, P4 ≥ 0 Non-negativity constraints.

(a) What are the ranges of optimality for the profit of Product 1, Product 2, Product 3, and Product 4?

(b) Find the shadow prices of the three constraints and interpret their meanings. What are the ranges in which each of these shadow prices is valid?

(c) If the profit contribution of Product 3 changes from $24 per unit to $50 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the sensitivity results given above. Do not solve the problem again).

(d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the sensitivity results given above. Do not solve the problem again).

Solve without using Microsoft Excel

Math   Statistics-And-Probability   
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