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: {Analyze Assertion (A)}
The graph shows that the line \( Z = x + 2y \) intersects the feasible region at corner points \( (60, 0) \) and \( (120, 60) \), yielding the identical maximum value. This implies the maximum value is attained at all points along the line segment connecting these two points. Therefore, Assertion (A) is true.

Step 2: {Analyze Reason (R)}
Typically, the optimal solution for a Linear Programming Problem (LPP) is found at the corner points of the feasible region. While this statement is generally correct, in this specific instance, the optimal solution extends along a line segment between two corner points. Consequently, Reason (R) does not accurately explain Assertion (A). 

Step 3: {Conclusion}
Both Assertion (A) and Reason (R) are true. However, Reason (R) is not a valid explanation for Assertion (A). Thus, the correct option is (B).