There are six cities $($cities $1-6)$ in Kilroy

County. The county must determine

where to build fire stations. Each city

also considered as the opening site of a

fire station. The county wants to build

the minimum number of fire stations

needed to ensure that at least one fire

station is within $15$ minutes $($driving

Time Required to Travel between Cities in Kilroy County

time$)$ of each city. The times required

to drive between the cities in Kilroy

County are shown in Table.

Formulate an IP that will tell Kilroy how

many fire stations should be built and

where they should be located.

Set Covering

Example $4$

Modify the model such that two fire stations must cover City $1.$

Suppose that a there is a fixed cost for opening a fire station. Modify the

model accordingly.

Suppose that city $4$ can be covered by only one fire station. Which part of

the model should be modified?

Suppose that if a fire station is opened at City $1,$ then a fire station must

open at City $2$ as well. Modify the model.