The mayor of Southport (IN) is thinking on redesigning its fire protection system in order to offer a better fire coverage. Actually, there is only one fire station, with a low coverage of the city. The mayor is planning to open new facilities in order to cover all the population of the city in T minutes. He doesn't know how many new facilities should be open and where to locate them. So far, he does not plan to close the existing facility.

1. Set a model that will help the mayor to find where to open the new facilities. Define all the indexes, parameters, decision variables, constraints and objective, and then formulate the problem.

2. Once the problem was solved, it was found that there is a need of locating 4 new facilities while keeping the existing one open. Since the budget for fire protection cannot cover for 4 facilities, the mayor has decided to open only 2 new facilities that will maximize the coverage of the population. The existing one remains open. Formulate the new problem.

3. Still not satisfied with the new solution, since some of the population remains uncovered and far from the fire stations, the mayor has decided to close the old station, and to locate 3 new fire stations so as to maximize coverage of the city in T minutes, with the additional constraint that all the population of the city should be covered in T+S minutes. Formulate the new problem.