In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y - 2x ≤ 0,y ≥ 0,0≤ x ≤ 5$. The feasible region of the above problem:

is bounded in the first quadrant

The correct answer is Option (1) → is bounded in the first quadrant

$\text{Constraints: }y-2x\le 0,\; y\ge 0,\; 0\le x\le 5$

From $0\le x\le 5$ and $y\ge 0$ with $y\le 2x$, for each $x\in[0,5]$ one has $0\le y\le 2x\le 10$. Hence both $x$ and $y$ are bounded and $y\ge0$ places the region in the first quadrant.

Answer: is bounded in the first quadrant