The feasible region represented by the system of inequalities \(x+y \le 3,\ y \le 6,\ x \ge 0,\ y \ge 0\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Bounded in first quadrant
The conditions x ≥ 0, y ≥ 0 keep the region in the first quadrant.
The line x + y = 3 meets the axes at (3, 0) and (0, 3). The inequality x + y ≤ 3 is the side containing the origin, since 0 + 0 ≤ 3.
So the region is the triangle with corners
\((0, 0),\ (3, 0),\ (0, 3)\)
In this triangle y ≤ 3, so the condition y ≤ 6 is automatically satisfied and adds nothing.
A triangle can be enclosed in a circle, so the feasible region is bounded and lies in the first quadrant.