The feasible region for an L.P.P is always a/an
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → convex set
Each linear constraint \( ax+by\le c \) (or \( \ge \)) is a half-plane, and a half-plane is a convex set. The feasible region is the common part of all these half-planes, and the intersection of convex sets is convex. So the feasible region of an L.P.P. is always a convex set.
Why the other options are incorrect
Option (1) concave set — Incorrect. A concave (non-convex) region has a dent; it cannot be the common part of half-planes.
Option (3) unbounded region — Incorrect. The feasible region may be bounded (a polygon) or unbounded; it is not always unbounded.
Option (4) bounded region — Incorrect. The feasible region may also be unbounded; it is not always bounded.
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
