Question

Assertion (A): Consider a Linear Programming Problem with minimise Z = x + 2y subject to constraints 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 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.

पर्याय

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (А).

• Both Assertion (A) and Reason (R) are a true, but Reason (R) is not the correct explanation of the Assertion (A).

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

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

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (А).

Explanation:

Assertion is true because substituting the corner points (0, 3) and (6, 0) into the objective function Z = x + 2y gives the same minimum value of 6 for both. Reason is also true and provides the correct explanation, as the objective function is parallel to the constraint line x + 2y = 6, meaning every point on that segment is an optimal solution.