Consider a transportation problem involving the set of sources S and the set of sinks T (cf. Example 1.4 in Ch. 1). Suppose that there is no strict subset S of S and strict subset T of T such that...

Consider a transportation problem involving the set of sources S and the set of sinks T (cf. Example 1.4 in Ch. 1). Suppose that there is no strict subset S of S and strict subset T of T such that

Show that for every feasible tree, the corresponding flow of every arc of the tree is positive. Conclude that for such a problem, starting from a feasible initial tree, degeneracy never arises in the simplex method.