Question

Assertion : 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 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 feasible region is crucial. If the feasible region is empty, it means there is no solution to the problem, as no point can satisfy all constraints simultaneously.

Answer 1

The Correct Option is A

- Assertion (A): An empty feasible region in a Linear Programming Problem signifies that the problem has no solution. This statement is correct. The feasible region comprises all points satisfying the problem's constraints. If this region is empty, no point simultaneously fulfills all constraints, thus indicating no solution exists.- Reason (R): The feasible region is defined as the area satisfying all constraints. This definition is accurate. It represents the set of points that adhere to all inequalities or equalities forming the problem's constraints. An empty feasible region implies that no point can satisfy all constraints concurrently.As both the Assertion (A) and the Reason (R) are accurate, and the Reason (R) provides a valid explanation for the Assertion (A), the appropriate response is option .