 Solution

A feasible point $x$ is an extreme point solution of a linear program if it cannot be written as a nontrivial convex combination of two distinct feasible points. Explicitly, ifthen $y=z=x$. Equivalently, $x$ lies in no open line segment joining two distinct feasible points. Being an extreme point concerns the feasible region; it does not by itself mean that $x$ optimizes the objective function.