The shaded part of the given figure indicates the feasible region. Then the constraints are
Show Hint
To pick out the correct constraints instantly, look at the outer flat limits. The region is blocked on the right at 5 and at the top at 3, so you must have $x \le 5$ and $y \le 3$. This allows you to eliminate options (B), (C), and (D) immediately without even testing the diagonal line!
Step 1: Understanding the Question:
The problem presents a linear programming graph showing a shaded geometric feasible region bounded by multiple lines. We need to identify the correct set of inequality constraints that define this exact shaded territory.
Step 2: Detailed Explanation:
Let's analyze the boundary lines of the region visible in the coordinate system step by step:
• The shaded region lies entirely within the first quadrant, meaning that both coordinates must be non-negative:
$$ x \ge 0, \quad y \ge 0 $$
• There is a vertical boundary line at $x = 5$. The shaded region lies to the left of this line, which translates to the inequality constraint:
$$ x \le 5 $$
• There is a horizontal boundary line at $y = 3$. The shaded region lies entirely underneath this line, which translates to the inequality constraint:
$$ y \le 3 $$
• There is a slanted boundary line passing through the origin representing the identity function $y = x$, which can be rewritten as the equation $x - y = 0$. The shaded feasible region lies below this line (closer to the x-axis, where $x$ values are greater than or equal to $y$ values). Testing a point inside the region like $(4, 1)$ gives $4 - 1 = 3 \ge 0$. This yields the inequality constraint:
$$ x - y \ge 0 $$
Combining all these individual boundaries together, our full set of constraints matches:
$$ x, y \ge 0; \quad x - y \ge 0; \quad x \le 5; \quad y \le 3 $$
Step 3: Final Answer:
The set of linear constraints bounding the shaded feasible region corresponds perfectly to option (A).
