= 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, if
$$
x=\lambda y+(1-\lambda)z,\qquad y,z\text{ feasible},\quad0<\lambda<1,
$$
then $y=z=x$. Equivalently, \b[$x$ 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>.
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