= Simplex optimality criterion
{title2=$z=z_0+\sum_j\bar c_jx_j$}
In a feasible minimization <simplex dictionary>, the nonbasic variables are nonnegative. If every <reduced cost> $\bar c_j\ge0$, the displayed objective identity proves $z\ge z_0$ for every feasible point. Thus the current <basic feasible solution> is globally optimal. If all <reduced costs> are strictly positive, equality forces every nonbasic variable to vanish and gives a unique basic solution, provided the dictionary determines all basic variables.
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