Question

Assertion (A): Every point of the feasible region of a Linear Programming Problem is an optimal solution.
Reason (R): The optimal solution for a Linear Programming Problem exists only at one or more corner point(s) of the feasible region.

• A. Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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, the optimal solution is always found at a corner point of the feasible region, not in the interior of the region.

Answer 1

The Correct Option is D

Step 1: Understanding the feasible region in Linear Programming.
In a Linear Programming Problem (LPP), the feasible region consists of all possible values that satisfy the given constraints. Step 2: Evaluating Assertion (A).
The optimal solution of an LPP is always found at one or more corner points of the feasible region, not at every point. Hence, Assertion (A) is false. Step 3: Evaluating Reason (R).
The Fundamental Theorem of Linear Programming states that the optimal solution lies at a corner point of the feasible region. This makes Reason (R) true.
Since Assertion (A) is false and Reason (R) is true, the correct answer is (D).