Question

Consider the following linear program: MIN Z = 60A + 50B s.t. 10A + 20B ≤...

Consider the following linear program: 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 using iso-profit method.

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Homework Answers

Answer #1

Given,

subject to,

The contraints are shown graphically below:

The feasible region is the area bound by the points shown on the graph.

Now the isoprofit line represented by is drawn on the graph and shown below:

We see that the isoprofit line passes through point (2,5). This gives the minimum value of Z

Hence, A= 2, B=5 and minimum value of Z is

Min Z = 60 x 2 + 50 x 5 = 120 + 250 = 370

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