CBSE 2025, Set 3

Question

**Assertion (A):** In a Linear Programming Problem, if the feasible region is empty, then the Linear Programming Problem has no solution.
**Reason (R):** A feasible region is defined as the region that satisfies all the constraints. A). Both Assertion (A) and Reason (R) are true and 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.

Edvaya · Accepted Answer

The correct answer is Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).. **Solution:**

**Assertion (A):** In a Linear Programming Problem (LPP), the optimal solution (if it exists) must lie within the feasible region. If the feasible region is empty (i.e., no points satisfy all the constraints simultaneously), then no possible solution can be evaluated, meaning the LPP has no solution. Thus, the assertion is **true**.

**Reason (R):** The feasible region is indeed defined as the set of all points that satisfy all constraints of the problem simultaneously. This is a fundamental concept in LPP and is **true**.

Since the non-existence of points satisfying all constraints (Reason) directly explains why an empty feasible region results in no solution (Assertion), **Reason (R) is the correct explanation of Assertion (A)**.

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Mathematics > Vectors And Linear Programming > Linear Programming

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