Where to build community libraries?
Johnson county plans to build new public libraries to serve its 7 towns/communities. Each library can serve communities within a maximum radius of 30 minutes’ drive. The following table shows the drive time between the 7 towns.
TO
FROM A B C D E F G
A 0 15 20 35 35 45 40
B 15 0 35 20 35 40 40
C 20 35 0 15 50 45 30
D 35 20 15 0 35 20 20
E 35 35 50 35 0 15 40
F 45 40 45 20 15 0 35
G 40 40 30 20 40 35 0
• What is the minimum number of libraries that would be needed and in which towns/communities should they be built (Formulate and solve it by Excel)?
• HINT: build your constraints by checking towns/communities within 30 minutes drive: make sure each community is served by at least one library
Community Communities within 30 minutes
A A, B, C
B A, B, D
C A, C, D, G
D B, C, D, F, G
E E, F
F D, E, F
G C, D, G