Solution
= Solution
{c}
Suppose the unique optimum $x^*$ were $(1-t)u+tv$ for distinct feasible points $u,v$ and $0<t<1$. Feasibility is preserved by convex combinations. Optimality gives $c^Tu\leq c^Tx^*$ and $c^Tv\leq c^Tx^*$, while linearity gives their strictly weighted average equal to $c^Tx^*$. Both inequalities must therefore be equalities. Then $u$ and $v$ are also optimal, contradicting uniqueness. Hence \b[the unique optimum is an <extreme point> of the feasible set].