The town of Lytle must determine how the best deploy four new emergency medical service vehciles among five existing EMS locations. The new vehicles differ in their hardware, and thus differ in their ability to respond to emergencies. The table below gives a “coverage rating” for each pair of vehicle and EMS location. The “coverage rating” is a function of capability of each vehicle and an estimate of the number of emergencies in the immediate area around each EMS location.
EMS Location: A, B, C, D, E
Vehicle 1: A-12,B-8,C-10, D-6, E-2
Vehicle 2: A-6,B-6,C-4,D-8, E-9
Vehicle 3: A-10, B-10, C-8, D-1, E-4
Vehicle 4: A-12, B-10, C-12, D-10, E-14
It has been determined that no EMS location would get more than one of the new vehicles. Further, for space considerations, Vehicle 4 cannot be assigned to location E. Also, Locations C and D cannot both get a new vehicle. Formulate this problem as a mathematical model with the goal of maximizing the “coverage” provided by the four new vehicles.