Solution:
The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is given below
O (0, 0), A (4, 0), and B (0, 4) are the corner points of the feasible region. The values of Z at these points are given below
| Corner point | Z = 3x + 4y | |
| O (0, 0) | 0 | |
| A (4, 0) | 12 | |
| B (0, 4) | 16 | Maximum |
Hence, the maximum value of Z is 16 at the point B (0, 4)