Use LP duality to prove the max-flow/min-cut theorem. That is, prove that the maximum s-t flow in a network is equal the total capacity of a minimum capacity cut. Hints: Write the classical dual of...

Use LP duality to prove the max-flow/min-cut theorem. That is, prove that the maximum s-t flow in a network is equal the total capacity of a minimum capacity cut. Hints: Write the classical dual of the maximum-flow problem (3.15). Let cut (S, T) correspond to a maximum flow, and define a dual feasible solution with respect to (S, T) that satisfies complementary slackness.