Why do the maximum and minimum values of feasible regions always occur at the vertices?

Question

 Why do the maximum and minimum values of feasible regions always occur at the vertices?

Answer 1

The maximum and minimum always values occur at the vertices because the vertex of a graph indicates the turning point of the values.  When the values increase then starts to decrease from left to right at a certain point, that point is the highest value (maximum) of the graph.  When the values decrease then starts to increase from left to right at a certain point, that point is the lowest value (minimum) of the graph.