The optimal value of the objective function is attained at the points

Given that,

• There is an objective function

• There are optimal values

From the definition of optimal value of a Linear Programming Problem(LPP):

An optimal/ feasible solution is any point in the feasible region that gives a maximum or minimum value if substituted in the objective function.

Here feasible region of an LPP is defined as:

A feasible region is that common region determined by all the constraints including the non-negative constraints of the LPP.

So the Feasible region of a LPP is a convex polygon where, its vertices (or corner points) determine the optimal values (either maximum/minimum) of the objective function.

For Example,

5x + y ≤ 100 ; x + y ≤ 60 ; x ≥ 0 ; y ≥ 0

The feasible solution of the LPP is given by the convex polygon OADC.

Here, points O, A ,D and C will be optimal solutions of the taken LPP

Hence the answer is option C.