Question: The following digraph shows a partially solved minimum cost network flow problem with node labels indicating net demand and arcs labels showing unit cost, capacity,

The following digraph shows a partially solved minimum cost network flow problem with node labels indicating net demand and arcs labels showing unit cost, capacity, and current flow.

(a) Verify that the current flow is feasible.

(b) Generate the six possible cycle directions of flow change.

(c) Verify for the first (one) of your cycle directions that a step l in the direction would leave flow balanced at all nodes.

(d) Determine whether each of your cycle directions is improving.

(e) Determine whether each of your cycle directions is feasible.

(f) For those directions that are feasible, compute the maximum step size l that could be applied without losing feasibility.

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