For a linear objective function under linear constraints, the optimal value must occur at a:

1. The objective function is linear, so it has no interior peak. 2. It increases steadily across the region in one direction. 3. The optimal value must occur at a corner point, or vertex, of the feasible region. 4. That is what makes testing only the vertices enough. _Source: syllabus Mathematics Part II, Ch 12 'Linear Programming'_