The feasible region corresponding to an LPP represented by the constraints \(x \ge 7,\ y \ge 4,\ x+2y \ge 8\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Unbounded and feasible
Every point with \(x \ge 7\) and \(y \ge 4\) also satisfies the third constraint:
\(x+2y \ge 7+2(4) = 15 \gt 8\)
So the constraint \(x+2y \ge 8\) is redundant, and the feasible region is simply
\(x \ge 7,\quad y \ge 4\)
This is the part of the plane to the right of the line x = 7 and above the line y = 4. It has one corner point, (7, 4), and extends without limit to the right and upwards.
The region contains points such as (7, 4), so it is feasible. It also contains (7 + k, 4) for every k ≥ 0, so no circle can enclose it: it is unbounded.
Why the other options are incorrect
Option (1) bounded and feasible — Incorrect. The region is feasible, but it extends without limit, so it is not bounded.
Option (3) bounded and not feasible — Incorrect. The point (7, 4) satisfies all three constraints, so the region is not empty; and it is not bounded.
Option (4) Concave polygon, unbounded and feasible — Incorrect. The region given by linear inequalities is always convex, never concave.