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Question

Minimise and Maximise Z = 5x + 10y

subject to.

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Solution

The feasible region determined by the constraints, x + 2y ≤ 120, x + y ≥ 60, x − 2y ≥ 0, x ≥ 0, and y ≥ 0, is as follows.

The corner points of the feasible region are A (60, 0), B (120, 0), C (60, 30), and D (40, 20).

The values of Z at these corner points are as follows.

Corner point

Z = 5x + 10y

A(60, 0)

300

→ Minimum

B(120, 0)

600

→ Maximum

C(60, 30)

600

→ Maximum

D(40, 20)

400

The minimum value of Z is 300 at (60, 0) and the maximum value of Z is 600 at all the points on the line segment joining (120, 0) and (60, 30).


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