Section II$.$ The following digraph shows a partially solved minimum cost network flow problem with node labels indicating net demand and acrs 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 $$ 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 $$ that could be applied without loosing feasibility.