duality and the max flow min-cut theorem in linear optimization

consider the maximum flow problem.
(a) Let pi be a price variable associated with the flow conservation constraint at node i . Let qij be price variable associated with the capacity constraint at arc (i,j). Write down a minimization problem, with variables pi and qij, whose dual is the maximum flow problem.
(b)show that the optimal value in the minimization problem is equal to the minimum cut capacity, and prove the max-flow min-cut theorem.

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