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Question 1

Maximise Z = 3x + 4y

Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0

Answer

The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is as follows.

The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4). The values of Z at these points are as follows.

Corner point

Z = 3x + 4y

 

O(0, 0)

0

 

A(4, 0)

12

 

B(0, 4)

16

→ Maximum

Therefore, the maximum value of Z is 16 at the point B (0, 4).

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