In an LPP, if the objective function \(z=ax +by\) has same maximum value at 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 occur at two corner points P and Q. Every point of the line segment PQ lies in the (convex) feasible region and can be written as tP + (1 − t)Q with 0 ≤ t ≤ 1. Since z is linear:
\(z\big(tP + (1 - t)Q\big) = t\,z(P) + (1 - t)\,z(Q)\)
\(= tM + (1 - t)M = M\)
So z takes its maximum value at every point of the segment PQ, that is, at infinitely many points.
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
