The feasible region (shaded) for a $LPP$ is shown in the adjacent figure. Maximize $Z = 5x + 7y$.
(N/A) The shaded region is bounded by the corner points $O(0,0)$,$A(7,0)$,$B(3,4)$,and $C(0,2)$.
We evaluate the objective function $Z = 5x + 7y$ at each corner point:
Comparing the values of $Z$,the maximum value is $43$,which occurs at the point $B(3,4)$.
We evaluate the objective function $Z = 5x + 7y$ at each corner point:
| Corner Point | Value of $Z = 5x + 7y$ |
|---|---|
| $O(0,0)$ | $5(0) + 7(0) = 0$ |
| $A(7,0)$ | $5(7) + 7(0) = 35$ |
| $B(3,4)$ | $5(3) + 7(4) = 15 + 28 = 43$ |
| $C(0,2)$ | $5(0) + 7(2) = 14$ |
Comparing the values of $Z$,the maximum value is $43$,which occurs at the point $B(3,4)$.
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