Suppose a new hospital is to be built to provide emergenct medical healthcare service to 5 town w coordinates (5,6), (1,3), 13,7), (11,2), (18,1) on a map. The exisiting transportation network for the region containing the 5 town allows only rectilinear travel:
1) Determine the coordinate of potential sites for hospital to be built at such distance of hospital to furthest town is minimizes. State any assumptions
2) If it is not possible to build hospital at site that have x coordinated less than 7 and a new hospital to be built at site identified from (1), which towns would be furthest away from hospital and what is this furthest distance?