In a linear programming problem, the constraints on decision variables \(x\) and \(y\) are \(y - 2x \le 0, y \ge 0, 0 \le x \le 5\). The feasible region of the above problem:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → is bounded in the first quadrant
The constraints say
\(0 \le y \le 2x,\quad 0 \le x \le 5\)
The region lies between the x-axis and the line y = 2x, from x = 0 to x = 5. It is the triangle with corner points
(0, 0), (5, 0), (5, 10)
Every point has \(0 \le x \le 5\) and \(0 \le y \le 10\), so the region is non-empty and bounded, and since \(x \ge 0, y \ge 0\) it lies in the first quadrant.