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