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:  Locations Areas A 1,4,7 B 1,3,5,7 C 1,2,5 D 2,5,6 E 3,4,7 F 4,6 Areas 2 and 6 must be covered by at least 2 locations. The rest of the areas must be covered by at least 1 location. What is the minimum number of locations?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section: Chapter Questions
Problem 80P
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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: 

Locations Areas
A 1,4,7
B 1,3,5,7
C 1,2,5
D 2,5,6
E 3,4,7
F 4,6

Areas 2 and 6 must be covered by at least 2 locations. The rest of the areas must be covered by at least 1 location.

What is the minimum number of locations?

 
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