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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).
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