### Prove the following min-flow max-cut theorem

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Minimum flow problem. The minimum flow problem is a close relative of the maximum flow problem with nonnegative lower bounds on arc flows. In the minimum flow problem, we wish to send the minimum amount of flow from the source to the sink, while satisfying given lower and upper bounds on arc flows.

(a) Show how to solve the minimum flow problem by using two applications of any maximum flow algorithm that applies to problems with zero lower bounds on arc flows. (Hint: First construct a feasible flow and then convert it into a minimum flow.)

(b) Prove the following min-flow max-cut theorem.

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