In a linear programming graph, the best (optimal) solution always occurs at a point called what?

The correct answer is:

An extreme point.

Explanation:

An extreme point is also called a corner point.

An optimal solution to a linear program is the feasible (reasonable) solution with the largest value, for a maximization problem.

Since we want the largest value, the corner point of the solution set would be optimal.

One of the facts of linear programming is that every linear program has an extreme point that is an optimal solution.