Minimise Z = – 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

It is given in the question that,

Z = - 3x + 4y

We have to subject on the following equation:

x +2y ≤ 8, 3x+2y ≤ 12, x ≥ 0, y ≤ 0

3x+2y ≤ 12

(x, y) = (0, 6), (4, 0)

x+2y ≤ 8

(x, y) = (0, 4), (8, 0)

We can clearly see that Z is minimum at (4, 0). Hence, minimum value of Z will be - 12

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