Given that,

The objective function will be maximum at ______

As per the steps while solving a Linear Programming Problem, we first determine the feasible region using the constraints and then, consider the vertices of the obtained convex polygon in the objective function to see the vertex at which the objective function obtains a maximum value. Then that vertex is determines the maximum value of the objective function.

Hence, the maximum value of an objective function under linear constraints is at any vertex of the feasible region.

Therefore the answer is C.