1.(The fixed charge net work design problem) we are given a directed graph G=(N,A) and a demand or supply bi for each i∈N, such that ∑bi=0, i∈N. There are two types of costs:transportation costs cij of shipping one unit from node i to node j,and building costs dij of establishing a link(i,j) between nodes i and node j of capacity uij. We would like to build such a network in order to minimize the total building and transportation costs, so that all demand is met. Formulate the problem as an integer programming problem.

2. (Facility location)For the facility location problem, prove that the inclusion PFL⊂PAFL can be strict.