A state government plans to set up new police stations for the public. The state has seven districts (A through G). Each police station can serve a radius of 30 miles. A district may receive service from more than one police station. The following tables shows the distance between the districts.

To From A B C D E F G A 0 16 21 31 32 46 40 B 31 0 35 24 31 31 31 C 21 35 0 22 27 32 33 D 32 33 22 0 28 31 35 E 30 36 27 0 25 35 F 46 28 32 26 25 0 18 G 40 27 33 20 24 32 0 The state wants to determine the number of police stations needed to cover all the districts.

a. Formulate an integer programming model for this problem.

b. Solve this model by using the computer.