Question

Assertion (A): The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP).
Reason (R): The region representing \( Z = 50x + 70y \) such that \( Z < 380 \) does not have any point common with 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 and the Reason (R) is 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:

When solving Linear Programming Problems, always check the intersection of the feasible region with the objective function's value to identify the point at which the minimum or maximum occurs.

Answer 1

The Correct Option is A

- The feasible region of a Linear Programming Problem (LPP) is the area satisfying all constraints, bounded by lines representing these constraints. The shaded area on the graph depicts this feasible region, validating Assertion (A).
- The objective function is \( Z = 50x + 70y \). Given that \( Z = 50x + 70y \) has a minimum value of 380 at point \( B(2, 4) \).
- If \( Z<380 \), the values of \( x \) and \( y \) lie outside the feasible region because the region defined by \( Z = 50x + 70y \) less than 380 does not overlap with the feasible region. Therefore, Reason (R) accurately explains the lack of intersection between the region \( Z<380 \) and the feasible region.
Conclusion: Both Assertion (A) and Reason (R) are correct, with Reason (R) providing the correct explanation for Assertion (A).