You are faced with locating ambulances in a city. You would like to find the locations of a fixed number of ambulance bases. Let P be the number you want to locate. You would like to maximize the number of demands (demands occur on nodes of the network) that can be covered within 5 min of the nearest ambulance. However, you require that the selected sites be such that all demand nodes can be covered by an ambulance within 10 min.

a) Using the notation we have defined for the set covering and maximum covering problems as well as any other notation you require, formulate this problem as an integer linear programming problem. Clearly define any new notation that you use. Clearly state in words what each of the constraints and the objective function is doing.

b) What can you say about the minimum value of P (the number of facilities to be located), which is an input, such that the problem will have a feasible solution?