| Corner point (x, y) | Value of the objective function Z = -50x + 20y |
| (0,5) | Z = - 50 $\times$ 0 + 20 $\times$ 5 = 100 |
| (0,3) | Z = - 50 $\times$ 0 + 20 $\times$ 3 = 60 |
| (1,0) | Z = - 50 $\times$ 1 + 20 $\times$ 0 = - 50 |
| (6,0) | Z = -50 $\times$ 6 + 20 $\times$ 0 = - 300 |
Clearly, - 300 is the smallest value of Z at the corner point (6, 0). Since the feasible region is unbounded, therefore, to check whether - 300 is the minimum value of Z, we draw the line - 300 = -50x + 20y and check whether the open half plane -50 x + 20y < -300 has points in common with the feasible region or not. From Fig., we find that the open half plane represented by - 50 x + 20y < - 300 has points in common with the feasible region. Therefore, Z = - 50x + 20y has no minimum value subject to the given constraints.
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| Machines | |||
| $I$ | $II$ | $III$ | |
| $A$ | $12$ | $18$ | $6$ |
| $B$ | $6$ | $0$ | $9$ |