Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table:

Potential Locations

for Substations Areas Covered

A .............1, 5, 7

B .............1, 2, 5, 7

C .............1, 3, 5

D .............2, 4, 5

E .............3, 4, 6

F ..............4, 5, 6

G ..............1, 5, 6, 7

a. Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas.

b. Solve the problem in part (a).