Question

The maximum value of $2x+y$ subject to $3x+5y\le 26$ and $5x+3y\le 30,x\ge 0,y\ge 0$ is

• A. 12
• B. 11.5
• C. 10
• D. 17.33

Answer 1

Answer: (A)

We have, Maximize
$Z=2x+y$
Subject to constraints
$3x+5y\le 26$
$5x+3y\le 30$
$x\ge 0,y\ge 0$
The graph of inequality are

Corner points	$Z=2x+y$
$(0,0)$	$Z=0$
$(0,\frac{26}{5})$	$Z=\frac{26}{5}=5.2$
$(6,0)$	$Z=12$ (Maximum)
$(\frac{9}{2},\frac{5}{2})$	$Z=\frac{18}{2}+\frac{5}{2}=\frac{23}{2}=11.5$

Maximum value $Z=12$