Question

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

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

Answer 1

Answer: (B)

Given : $x +2 y \geq 2\,\,\, ...(1)$
$x +2 y \leq 8\,\,\, ...(2)$
and $x , y \geq 0$
For equation (1)
$\frac{ x }{2}+\frac{ y }{1}=1$ and for equation ( 2 )
$\frac{ x }{8}+\frac{ y }{4}=1$
Given : $z =3 x +2 y$
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 $(8,0)$