Question: The digraph below shows a minimum cost network flow instance. Labels on arcs are (cost, capacity, current flow. Labels on the nodes show net demand.

The digraph below shows a minimum cost network flow instance. Labels on arcs are (cost, capacity, current flow. Labels on the nodes show net demand.

(a) Establish that the given flow is feasible.

(b) Start from the given solution and solve the instance to optimality by the Cycle Cancelling Algorithm 10B. Show the residual digraph at each step, but choose improving feasible cycle directions from them by inspection.

(c) Compute bound 10.26 on the Algorithm 10B computational effort for this instance and compare to the number of steps in your solution of part (b).

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