Question

Two statements are provided: an Assertion (A) and a Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) given below: Assertion (A): Consider a Linear Programming Problem with minimise $Z = x + 2y$ subject to constraints $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$ which gives minimum $Z$ at infinitely many points. The corner points of feasible region are $(0, 3)$ and $(6, 0)$.
Reason (R): If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

• 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.

Hint:

When the coefficients of the variables in the objective function $Z = ax + by$ are perfectly proportional to the coefficients of a bounding constraint line $ax + by = c$, the optimal solution will always occur along the entire corresponding line segment, generating infinitely many solutions.

Answer 1

The Correct Option is A