PROBLEM 4 (25 points) Suppose there are six cities in Butler County. The county must determine where to build charge stations for electric vehicles. Specifically, it wants to build the minimum number of charge stations needed to ensure that at least one station is within 20 minutes driving time) of each city. Assume that the charge stations can only be built in the cities themselves, and that the cost of building a station in any of the six cities is the same (assume $1 for simplicity). The following table indicates which cities are within 20 minutes of the given city: City 1 City 2 City 3 City 4 City 5 City 6 Cities within 20 minutes City 1, City 2 City 1, City 2, City 6 City 3, City 4 City 3, City 4, City 5 City 4, City 5, City 6 City 2, City 5, City 6 Formulate an integer program that will minimize the number of charge stations needed to service all six cities