Question

The feasible region of an LPP is shown in the figure. If $Z=11x+7y$, then the maximum value of $Z$ occurs at

• A. (0,5)
• B. (3,3)
• C. (5,0)
• D. (3,2)

Answer 1

Answer: (D)

$y$ Intercept of $x+y=5$ is $(0,5)$
$y$ -intercept of $x+3y=9$ is $(0,3)$
The intersection point of $x+y=5$ and $x+3y=9$ is $(3,2)$
Therefore, the corner points are $(0,5),(0,3),(3,2)$
At $(0,5),Z=35$
At $(0,3),Z=21$
At $(3,2),Z=47$
So, $Z_{\max }=47$ at $(3,2)$.