I. (20 pts) Given a directed graph G = (VE) with capacity c(u, u) > 0 for each edge (u,v) E E and demand r(v) at each vertex v E V, a routing of flow is a function f such that for all u, v) E E, 0 0 at each edge (u, v), and we are looking for a routing f satisfying f(u, v) 2 l(u, v) for all (u, v) E E Show how to find such a routing or determine that one does not exist by reducing to a maximum flow