Question 2 There are 6 cities inKilroy County.ﾃつﾃつThe county must determine where to buildcentral fire stations.ﾃつﾃつ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 drive between thecities in Kilroy County are given in the table. Formulate a modelthat will tell Kilroy how many fire stations should be built andwhere 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.
