Question

If $x+y\le 2$ ; $x\ge 0,y\ge 0$ is the point at which maximum value of $3x+2y$ attained will be:

• A. $\left(0,2\right)$
• B. $\left(0,0\right)$
• C. $\left(2,0\right)$
• D. $\left(\frac{1}{2},\frac{1}{2}\right)$

Answer 1

The correct option is C

$\left(2,0\right)$

Explanation for the correct option.

Step 1: Draw graph for $x+y\le 2$.

Taking $x+y=2$

$x$	$0$	$1$	$2$
$y$	$2$	$1$	$0$

As $x+y\le 2$, so shading will be towards origin.

Step 3: Find the point where $3x+2y$ is maximum.

At $\left(0,2\right)$, $3x+2y=3\left(0\right)+2\left(4\right)=4$

At $\left(1,1\right)$, $3x+2y=3\left(1\right)+2\left(1\right)=5$

At $\left(0,0\right)$, $3x+2y=3\left(0\right)+2\left(0\right)=0$

At $\left(2,0\right)$, $3x+2y=3\left(2\right)+2\left(0\right)=6$

So, $3x+2y$ is maximum at $\left(2,0\right)$.

Hence, option C is correct.