The following digraph depicts a partially solved minimum cost flow problem with labels on the nodes indicating net demand and those on the arcs showing unit cost, capacity, and current flow.

(a) Verify that the given solution is a basic feasible solution for basis 511, 22, 11, 32, 13, 426.

(b) Identify a cycle for which the corresponding cycle direction could be pursued by cycle cancelling Algorithm 10B but not by network simplex Algorithm 10C with the basis of part (a).

(c) Identify a cycle for which the corresponding cycle direction could be pursued by network simplex Algorithm 10C with the basis of part

(a) but not by cycle cancelling Algorithm 10B.