In an LPP if the objective function \(z = ax + by\) has same maximum value on two corner points of the feasible region, then the number of points at which maximum value of z occurs is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Infinite
Let the maximum value M be reached at two corner points P and Q. Every point of the segment PQ can be written as
\(R = (1 - \lambda)P + \lambda Q, \quad 0 \le \lambda \le 1\)
Since z = ax + by is linear,
\(z(R) = (1 - \lambda)z(P) + \lambda z(Q)\)
\(= (1 - \lambda)M + \lambda M = M\)
So z has the same maximum value at every point of the segment joining the two corners, not only at the corners. A segment has infinitely many points, so the maximum occurs at infinitely many points (alternate optimal solutions).
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
