Consider the following problem. You are faced with locating fire stations in a city. You would like to find the locations of a fixed number of stations. Let P be the number you want to locate. You...

Consider the following problem. You are faced with locating fire stations in a city. You would like to find the locations of a fixed number of stations. Let P be the number you want to locate. You would like to maximize the number of demands that can be covered within 4 min of the nearest station. Demands occur on the nodes of the network. You require that the selected sites be such that 90% the demand nodes can be covered by an ambulance within 8 min.

(a) Using the notation defined in the text 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) Qualitatively describe how the objective function (maximizing the number of demands that can be covered within 4 min) will change if we change the requirement that 90% of the demand nodes be covered within 8 min to a requirement that 90% be covered within 10 min. Justify your answer briefly.