Question

The maximum value of $z=3x+2y$ subject to $x+2y\ge 2,x+2y\le 8,x,y\ge 0$ is :

• A. 32
• B. 24
• C. 40
• D. None of these

Answer 1

Answer: (B)

Given : $x+2y\ge 2...(1)$
$x+2y\le 8...(2)$
and $x,y\ge 0$
For equation (1)
$\frac{x}{2}+\frac{y}{1}=1$ and for equation ( 2 )
$\frac{x}{8}+\frac{y}{4}=1$
Given : $z=3x+2y$
At point $(2,0);z=3\times 2+0=6$
At point $(0,1);z=3\times 0+2\times 1=2$
At point $(8,0);z=3\times 8+2\times 0=24$
At point $(0,4);z=3\times 0+2\times 4=8$
$\therefore$ maximum value of $z$ is $24$ at point $(8,0)$