Question

If $Z=3x+4y,$ subject to the constraints: $x+y\le 4,$ $x\ge 0,$ $y\ge 0,$ then $Z_{max}$ is equal to

• A. $24$
• B. $12$
• C. $20$
• D. $16$

Answer 1

The correct option is D $16$

The feasible region determined by the constraints $x+y\le 4,x\ge 0,y\ge 0$ is as follows.


The corner points of the feasible region are $O(0,0),A(4,0)$ and $B(0,4)$. The values of $Z$ at these points are as follows.

Corner points	$Z=3x+4y$
$O(0,0)$	$0$
$A(4,0)$	$12$
$B(0,4)$	$16\to \text{maximum}$

Hence, the maximum value of $Z$ is $16$ at the point $B(0,4).$