Verify that (4.11) is the dual problem after the change of variable u˜ = uB − cB. Write the classical dual of the minimum cost network flow problem (3.11). Show that if x and u are primal and dual...

Verify that (4.11) is the dual problem after the change of variable

u˜ = uB − cB.

Write the classical dual of the minimum cost network flow problem

(3.11). Show that if x and u are primal and dual feasible, respectively, then

x satisfies the optimality conditions for the network flow problem.