Proof of Finite Number of Basic Feasible Solutions

Students often struggle to differentiate between a 'basic solution' (which only requires

x_N=0

and

B

to be invertible) and a 'basic *feasible* solution' (which additionally requires

x_B \ge 0

). The

\binom{n}{m}

bound is an upper limit, not an exact count, as many basic solutions may not be feasible, or multiple bases can correspond to the same geometric vertex (degeneracy).

Institutional Reference: Linear and Integer Programming

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