Question

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Answer 1

(1) Let us first consider the linear equation $3x+2y=48$.

We observe that the shaded region and origin both are on same side of this line and $(0,0)$ satisfies $3x+2y\le 48$.

Therefore, we must have $3x+2y\le 48$

as linear inequality corresponding to the line $3x+2y=48$ .

(2) Consider the linear equation

We observe that the shaded region and origin both are on same side of this line and $(0,0)$ satisfies $x+y\le 20$.

Therefore, we must have $x+y\le 20$ as linear inequality corresponding to the line $x+y=20$

(3) Also, the shaded region lies in the first quadrant only.

Therefore, $x\ge 0,y\ge 0$

Hence, the required linear inequalities are,

$3x+2y\le 48$, $x+y\le 20$, $x\ge 0,y\ge 0$