Step 1 (Governing Principle & Given Data): [0.25 Mark]

The problem requires identifying the nature of the feasible region defined by a system of linear inequalities in the Cartesian plane. The given constraints are:

• $3x + y \geq 3$
• $2x - y \geq -5$
• $x \geq 0, y \geq 0$ (First Quadrant constraint)

Step 2 (Step-by-Step Mathematical Working): [0.50 Mark]

We analyze the boundaries and the region:

• The constraint $x, y \geq 0$ restricts the feasible region strictly to the first quadrant.
• For $3x + y \geq 3$: The line passes through $(1, 0)$ and $(0, 3)$. The region is away from the origin.
• For $2x - y \geq -5$ (or $y \leq 2x + 5$): The line passes through $(0, 5)$ and $(-2.5, 0)$.
• As $x \to \infty$, the value of $y$ for both lines increases or remains positive. Specifically, since there is no upper bound constraint (like $x \leq k$ or $y \leq k$), the region extends infinitely as $x$ and $y$ increase.
• Since the region is restricted to the first quadrant and extends infinitely towards the positive $x$ and $y$ axes, it is unbounded.

Step 3 (Final Concluded Answer): [0.25 Mark]

Comparing the analysis with the given options, the region is unbounded and lies in the first quadrant. Therefore, the correct option is (A).

💡 EL10 Concept Insight: Imagine you are standing in the corner of a room (the first quadrant) and you have to stay away from two walls; because there is no ceiling or far wall to stop you, you can keep walking forever in the open space, which is why we call the area "unbounded."