Which of the following is incorrect about the Linear Programming Problem (LPP)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → If the feasible region is unbounded, then a minimum value of the objective function always exists.
Each option is checked as a statement; the answer is the statement that is false.
Option (1) If the feasible region R of a Linear Programming Problem (LPP) is bounded, then the objective function has both a maximum and a minimum value in R. — Correct. This is the corner point theorem: on a bounded region both values exist and occur at corner points.
Option (2) An LPP can have no solution or more than one optimal solution. — Correct. If the constraints have no common region there is no solution; if the objective line is parallel to an edge of the region, there are infinitely many optimal solutions.
Option (3) If two corner points of the feasible region are both optimal solutions of the same type, then any point on the line segment joining these two points is also an optimal solution of the same type. — Correct. Z is linear, so it keeps the same value along the segment joining two points where it has that value.
Option (4) If the feasible region is unbounded, then a minimum value of the objective function always exists. — Incorrect. On an unbounded region an optimal value may not exist. For example, minimise \(Z = -x\) subject to \(x \ge 0,\ y \ge 0\): Z decreases without limit as x increases.
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
