Question

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

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

Answer 1

The correct option is A $(0,0)$

$x\le 0$ and $y\le 0$ represents third Quadrant

$x+y\le 2$ represents the region below the line $x+y\le 2$ $($ the region which contains origin$)$

The common region of given set of equations is third quadrant $($ including negative $x$ axis and negative $y$ axis$)$

Since $x$ and $y$ values are $\le 0$ in the third quadrant , the maximum value of $3x+2y$ occurs at $x=0$ and $y=0$ and the maximum value is $0$

Therefore the correct option is $A$