Question

Assertion (A): The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of \( Z = x + 2y \) occurs at infinite points. 
Reason (R): The optimal solution of a LPP having bounded feasible region must occur at corner points. 
 

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

In linear programming, always check if the objective function is constant along any edge of the feasible region.

Answer 1

The Correct Option is B

Step 1: Evaluate Assertion (A)
The graph reveals that the line \( Z = x + 2y \) intersects the feasible region at two corner points, \( (60, 0) \) and \( (120, 60) \), yielding identical maximum values. This implies that the maximum value is achieved at infinitely many points along the segment connecting these two points. Therefore, Assertion (A) is correct.
Step 2: Evaluate Reason (R)
The general principle states that the optimal solution for a Linear Programming Problem (LPP) is found at the corner points of the feasible region. While this statement is true, in this specific instance, the optimal solution is distributed along a line segment connecting two corner points. Consequently, Reason (R) does not adequately explain Assertion (A).
Step 3: Final Determination
Both Assertion (A) and Reason (R) are valid statements. However, Reason (R) does not provide the correct justification for Assertion (A). Thus, option (B) is the appropriate choice.