Linear Inequalities

Concept:The shaded region is the intersection of half-planes determined by the given lines and the axes.Explanation:The lines are $L_1: x+2y=3$, $L_2: x+y=4$, $L_3: x=\frac{5}{2}$, $L_4: y=\frac{3}{2}$.The shaded region is a triangle with vertices at $(0,\frac{3}{2})$ (intersection of $L_1$ and $L_4$), $(\frac{5}{2},\frac{3}{2})$ (intersection of $L_2$, $L_3$, $L_4$), and $(\frac{5}{2},\frac{1}{4})$ (intersection of $L_1$ and $L_3$).This triangle lies above $L_1$ (so $x+2y \ge 3$) and below $L_2$ (so $x+y \le 4$).The region is also bounded by the axes and the vertical/horizontal lines, giving $0 \le x \le \frac{5}{2}$, $0 \le y \le \frac{3}{2}$, and $x \ge 0, y \ge 0$.Answer:Option A is correct.