Question

In an LPP, if the objective function \( Z = ax + by \) has the same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of \( Z \) occurs is:

• A. \( 0 \)
• B. \( 2 \)
• C. \( {finite} \)
• D. \( {infinite} \)

Hint:

In LPP, when the optimal value occurs at two corner points, it implies that all points on the line segment joining these two points yield the same value.

Answer 1

The Correct Option is D

Step 1: In a Linear Programming Problem (LPP), if the objective function \( Z = ax + by \) has the same value at two corner points of the feasible region, then the maximum value of \( Z \) will occur at all points on the line segment joining these two corner points. 
Step 2: Since the line segment contains infinitely many points, the number of points at which \( Z \) attains its maximum value is infinite.