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Question 1

# Maximise Z = 3x + 4ySubject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0

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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