Question

Assertion (A): The corner points of the bounded feasible region of a L.P.P. are shown below. The maximum value of Z = x + 2y occurs at infinite points.

Reason (R): The optimal solution of a LPP having bounded feasible region must occur at corner points.

Options

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

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

Explanation:

Assertion (A): The maximum value of Z = x + 2y occurs at infinite points.
If Z = x + 2y achieves the same maximum value along an entire edge of the feasible region, then there are infinite solutions. Otherwise, the maximum occurs only at a single corner point.

Reason (R): The optimal solution of an LPP having a bounded feasible region must occur at corner points. However, if the objective function is parallel to one of the boundary lines of the feasible region, the maximum (or minimum) value occurs at multiple points along that edge.