CBSE 2025, Set 2

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 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 Assertion (A) is false, but Reason (R) is true.. **Solution:**

**Reason (R):** According to the Fundamental Theorem of Linear Programming, if an optimal solution (maximum or minimum) exists for the objective function, it must occur at a corner point (vertex) of the feasible region. Therefore, Reason (R) is **true**.

**Assertion (A):** The feasible region consists of infinitely many points that satisfy all the constraints. However, only the specific corner point(s) (or points on the line segment joining two optimal corner points) yield the *optimal* (max/min) value of the objective function. Every point in the region is a *feasible* solution, but not an *optimal* solution. Therefore, Assertion (A) is **false**.

Therefore, Assertion (A) is false, but Reason (R) is true.

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Mathematics > Vectors And Linear Programming > Linear Programming

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