Step 1 (Governing Law & Given Data): [1/4 Mark]

To determine the constraints of a Linear Programming Problem (LPP) from a graph, we identify the equations of the boundary lines using the intercept form: $$\frac{x}{a} + \frac{y}{b} = 1$$ where $a$ and $b$ are the $x$ and $y$ intercepts respectively. The inequality sign ($\le$ or $\ge$) is determined by the side of the line containing the feasible region (usually tested by the origin $(0,0)$).

Step 2 (Step-by-Step Mathematical Working): [1/2 Mark]

• Line 1: Passes through $(5, 0)$ and $(0, 5)$. $$\frac{x}{5} + \frac{y}{5} = 1 \implies x + y = 5$$ Since the feasible region is towards the origin (or below the line), the constraint is $x + y \le 5$.
• Line 2: Passes through $(9, 0)$ and $(0, 3)$. $$\frac{x}{9} + \frac{y}{3} = 1 \implies x + 3y = 9$$ Since the feasible region is towards the origin (or below the line), the constraint is $x + 3y \le 9$.

Step 3 (Final Concluded Answer): [1/4 Mark]

Comparing the derived constraints with the given options, we find that both inequalities are of the "less than or equal to" type. Therefore, the correct option is (A).

💡 EL10 Concept Insight: Think of the constraints as "fences" around a yard; if the shaded area is on the side of the fence closest to the corner $(0,0)$, it means the values are "less than" the boundary, so we use the $\le$ sign.