Given: Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2, x ≥ 0, y ≥ 0.
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 corner points O(0, 0), A(3, 0), B(3, 2) 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 maximum value of Z is 47.
Therefore, the maximum value of the function Z is 47 at (3, 2).
