Cook County has six communities that need to be served by fire stations. The number of minutes it takes to travel between communities is shown in Table 1. The county would like to establish the minimum number of fire stations so that each community can get a response in five minutes or less. Table 1: Travel times A B D E F A 4 6 3 5 8 B 4 0 4 10 6 5 C 6 4 0 9 3 5 3 10 9 0 6 3 E 5 6 6 0 10 8 5 5 3 10 0 a) (10 marks] Formulate a linear mathematical model that determines the minimum number of fire stations needed. b) Write down the necessary constraints for each of the following situations: i) [4 marks] It is not possible to establish fire stations in both communities A and C. ii) [3 marks) At most two communities among B, D, E, and F can be chosen to establish fire stations. iii) [3 marks) If community E is chosen, then F must also be chosen