2. (Capacitated facility location problem) Suppose we are given n potential facility locations and a list of m clients who need to be serviced from these locations. There is a fixed cost f; of opening a facility at location j, and service capacity of location j is limited to U;. Client i has demand quantity d, and the transportation cost to service unit demand of client i from facility j is Cij. The goal is to select a set of facility locations to establish facilites and determine the transportation quantity to the clients from facilities, while minimizing the total cost. Client demands should be met exactly and the capacity limit of facilites must be observed. Formulate the capacitated facility location problem as an integer program