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 : In a Linear Programming Problem, if the feasible region is empty, then the Linear Programming Problem has no solution. This assertion is true. The feasible region represents the set of all points that satisfy the given constraints of the Linear Programming Problem. If the feasible region is empty, it means that no solution exists that satisfies all the constraints simultaneously. Hence, the Linear Programming Problem has no solution when the feasible region is empty. - Reason (R): A feasible region is defined as the region that satisfies all the constraints. This is also true. The feasible region represents all the points that satisfy the system of inequalities or equalities that define the constraints of the Linear Programming Problem. If this region is empty, no solution can be found that satisfies all constraints. Since both Assertion and Reason (R) are true, and Reason (R) correctly explains Assertion , the correct answer is option .