Linear Inequalities

Concept:The feasible region is the intersection of half-planes defined by the inequalities in the first quadrant.Explanation:Rewrite the inequalities as $x + 2y \le 5$, $x + y \ge 1$, $x \ge 0$, $y \ge 0$.Draw the boundary lines:$x + 2y = 5$ passes through $(5,0)$ and $(0,2.5)$, shade below.$x + y = 1$ passes through $(1,0)$ and $(0,1)$, shade above.Also $x \ge 0$ and $y \ge 0$ restrict to the first quadrant.The intersection of these half-planes yields a quadrilateral region with vertices:$(1,0)$ on the x‑axis, $(5,0)$ on the x‑axis, $(0,2.5)$ on the y‑axis, and $(0,1)$ on the y‑axis.Answer:The region is the quadrilateral bounded by these four points. Among the given options, the correct graph is option B.