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).