Linear Inequalities

Concept:Identify the system of linear inequalities that represents the given shaded region.Explanation:The shaded region is bounded by the lines $L_1: x+y=30$, $L_2: x-y=0$, $L_3: x=20$, $L_4: y=12$, $L_5: y=3$, and the axes $x=0$, $y=0$.The region lies below $L_1$ (since shading is towards smaller $x+y$), so $x+y \le 30$.The region lies to the right of $L_2$ (where $x \ge y$), so $x-y \ge 0$.$x$ is bounded left by $x=0$ and right by $x=20$, giving $0 \le x \le 20$.$y$ is bounded below by $y=3$ and above by $y=12$, giving $3 \le y \le 12$.Non‑negativity $x \ge 0$, $y \ge 0$ holds.All inequalities correspond to option A.Answer:Option A: $x+y \leq 30$, $x-y \geq 0$, $0 \leq x \leq 20$, $3 \leq y \leq 12$, $x \geq 0$, $y \geq 0$.