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 enumeration method.

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Homework Answers

Answer #1

Solution by graphical method is as follows:

Variables A and B are plotted along X and Y axes respectively.

Feasible region is the shaded quadrilateral bounded by corner points as shown on the graph.

Corner points are: (2, 5), (6.875, 5), (5.455, 7.273), (2, 9)

Using enumeration method, value of objective function is computed at each of the corner points.

A B Objective value
2 5 370
6.875 5 662.5
5.455 7.273 690.95
2 9 570

The minimum value of objective function is 370 at corner point (2,5)

Therefore, optimal solution is:

A = 2

B = 5

Value of Z = 60*2+50*5 = 370

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