The feasible region for a $LPP$ is shown in the figure. Find the minimum value of $Z=11x+7y$.
(A) The lines $x+y=5$ and $x+3y=9$ intersect at $(3,2)$. From the figure,the feasible region is bounded with corner points $C(0,3)$,$A(3,2)$,and $B(0,5)$.
We evaluate the objective function $Z=11x+7y$ at each corner point:
Comparing the values of $Z$,the minimum value is $21$ at the point $(0,3)$.
We evaluate the objective function $Z=11x+7y$ at each corner point:
| Corner Point | Value of $Z=11x+7y$ |
| $C(0,3)$ | $11(0)+7(3) = 21$ |
| $A(3,2)$ | $11(3)+7(2) = 33+14 = 47$ |
| $B(0,5)$ | $11(0)+7(5) = 35$ |
Comparing the values of $Z$,the minimum value is $21$ at the point $(0,3)$.
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