Question

Minimise Z = 13x – 15y subject to the constraints: x + y ≤ 7, 2x – 3y + 6 ≥ 0, x ≥ 0, y ≥ 0.

Answer 1

Given: Z = 13x – 15y subject to the constraints: x + y ≤ 7, 2x – 3y + 6 ≥ 0, x ≥ 0, y ≥ 0.

Taking x + y = 7, we have

Now, plotting all the constrain equations we see that the shaded area OABC is the feasible region determined by the constraints.

The feasible region is bounded with four corners O(0, 0), A(7, 0), B(3, 4) and C(0, 2).

So, the maximum value can occur at any corner.

On evaluating the value of Z, we get

From the above table it’s seen that the minimum value of Z is -30.

Therefore, the minimum value of the function Z is -30 at (0, 2).