Question

MIN Z = 60A + 50B s.t. 10A + 20B ≤ 200 8A + 5B ≤ 80 A ≥ 2 B ≥ 5 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

Answer 1

The minimum value of the objective function Min Z = 60A + 50B is 229

How to find the minimum value of the objective function

From the question, we have the following parameters that can be used in our computation:

Min Z = 60A + 50B

Subject to:

10A + 20B ≤ 200

8A + 5B ≤ 80

A ≥ 2 B ≥ 5

From the graph, we have the following coordinates of optimal region

(x, y) = (2, 2.18), (2, 9) and (5.5, 7.3)

Recall that

Z = 60A + 50B

So, we have

Z = 60 * 2 + 50 * 2.18 = 229

Z = 60 * 2 + 50 * 9 = 570

Z = 60 * 5.5 + 50 * 7.3 = 695

Hence, the minimum value of the objective function is 229