In an LPP, the feasible region represented by the set of constraints \(2x + 3y \le 18, x + y \le 10, x \ge 0, y \ge 0\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Region A
The feasible region is the set of points that satisfy all the constraints together. With \(x \ge 0, y \ge 0\) it lies in the first quadrant.
The line \(2x + 3y = 18\) passes through (9, 0) and (0, 6). The origin gives \(0 \le 18\), so \(2x + 3y \le 18\) is the side of this line that contains the origin.
The line \(x + y = 10\) passes through (10, 0) and (0, 10). The origin gives \(0 \le 10\), so \(x + y \le 10\) is also the side containing the origin.
Region A lies below both lines, so it satisfies every constraint. Region B lies above the line \(2x + 3y = 18\): for example (8, 1) in B gives \(2x + 3y = 19 \gt 18\). Region C lies above \(x + y = 10\) as well.
So the feasible region is Region A only.