QDM Question 2 There are 6 cities inKilroy County. The county must determine where to buildcentral fire stations. The county wants to build theminimum number of central fire stations needed to ensure that atleast two fire stations are within 20 minutes (driving time) ofeach city. The times (in minutes) required to drivebetween the cities in Kilroy County are given in the table.Formulate a model that will tell Kilroy how many fire stationsshould be built and where they should be located.
From | To |
City 1 | City 2 | City 3 | City 4 | City 5 | City 6 |
City 1 | 0 | 10 | 20 | 30 | 30 | 20 |
City 2 | 10 | 0 | 25 | 35 | 20 | 10 |
City 3 | 20 | 25 | 0 | 15 | 30 | 20 |
City 4 | 30 | 35 | 15 | 0 | 15 | 25 |
City 5 | 30 | 20 | 30 | 15 | 0 | 14 |
City 6 | 20 | 10 | 20 | 25 | 14 | 0 |
Decision variables (1 mark):
Objective function (1 mark):
Constraints :
Additional constraint : Either City 1 or City 2 (or both)must be selected to build a fire station in if both City 3 and City4 are selected to build fire stations in.
