Question

The feasible region for the constraints $ x - y \ge 0, x - 5y \le -5, x \ge 0, y \ge 0 $ is shown by the figure:

• A. A
• B. B
• C. C
• D. D

Hint:

Test a point (like (5,1)) in the inequalities to quickly verify which side of the line to shade.

Answer 1

The Correct Option is B

Step 1: Analyze $x - y \ge 0$
This gives $x \ge y$, i.e., $y \le x$. The region lies on or below the line $y = x$.

Step 2: Analyze $x - 5y \le -5$
Rearranging, we get $5y \ge x + 5$ or $y \ge \frac{x}{5} + 1$. The boundary line passes through the intercepts $(-5, 0)$ and $(0, 1)$. The region lies on or above this line.

Step 3: Non-negativity constraints
$x \ge 0,\; y \ge 0$ restrict the solution to the first quadrant.

Step 4: Conclusion
The feasible region is the area in the first quadrant that lies below the line $y = x$ and above the line $y = \frac{x}{5} + 1$. This corresponds to the unbounded region shown in figure (B).
Final Answer: (B)