Question

The feasible region for the constraints \( x - 2 \le y, x \ge y - 1, x \ge 2, y \le 4, x, y \ge 0 \), is

• A. A
• B. B
• C. C
• D. D

Hint:

Always test the origin $(0,0)$ in inequalities to quickly determine which side of the line to shade.

Answer 1

The Correct Option is A

Step 1: Concept
The feasible region is the intersection of all half-planes defined by the given linear inequalities.

Step 2: Meaning
Each inequality represents a boundary line and a side of that line. $x \ge 2$ and $y \le 4$ define vertical and horizontal boundaries.

Step 3: Analysis
The lines are $x - y = 2$, $x - y = -1$, $x = 2$, and $y = 4$. Testing $(0,0)$ in $x - y \le 2$ (True) and $x - y \ge -1$ (True) shows the region lies between the two parallel diagonal lines.

Step 4: Conclusion
By plotting these boundaries, the bounded polygon matches the graphical representation in option (A). Final Answer: (A)