Question -
Answer -
The feasible region determined by the system of constraints, x +3y ≥ 3, x + y ≥ 2, and x, y ≥ 0 is given below
It can be seen that the feasible region is unbounded.
The corner points of the feasible region are A (3, 0), B (3 / 2,1 / 2) and C (0, 2)
The values of Z at these corner points are given below
| Corner point | Z = 3x + 5y | |
| A (3, 0) | 9 | |
| B (3 / 2, 1 / 2) | 7 | Smallest |
| C (0, 2) | 10 | |
7 may or may not be the minimum value of Z because the feasibleregion is unbounded
For this purpose, we draw the graph of the inequality, 3x + 5y< 7 and check the resulting half plane have common points with the feasibleregion or not
Hence, it can be seen that the feasible region has no commonpoint with 3x + 5y < 7
Thus, the minimum value of Z is 7 at point B (3 / 2, 1 / 2)