Given a flow network G(V, E), for every edge(u, v)

(15 pts) Given a flow network G(V, E), for every edge (u, v), I(u, v) is the lower bound on flow from node u to node v; c(u, v) is the upper bound on flow from node u to node v; e(u, v) is the expense for sending a unit of flow on (u, v). Formulate an LP and show that if it has an optimal solution, the optimal solution corresponds to a flow that satisfies lower bounds and upper bounds on all edges and minimizes the total expense. The total expense is the sum of expenses on all edges. (15 pts) Given a flow network G(V, E), for every edge (u, v), I(u, v) is the lower bound on flow from node u to node v; c(u, v) is the upper bound on flow from node u to node v; e(u, v) is the expense for sending a unit of flow on (u, v). Formulate an LP and show that if it has an optimal solution, the optimal solution corresponds to a flow that satisfies lower bounds and upper bounds on all edges and minimizes the total expense. The total expense is the sum of expenses on all edges