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.