The municipality of Cafetown would like to decide where to locate the two fire stations that have been allocated to the community. For planning purposes, Cafetown has been divided into five tracts, with no more than one fire station to be located in any given tract. Each station is to respond to all the fires that occur in the tract in which it is located as well as in the other tracts that are assigned to this station. Thus, the decisions to be made consist of (1) the tracts to receive a fire station and (2) the assignment of each of the other tracts to one of the fire stations. The objective is to minimize the overall average of the response times to fires.

The following table gives the average response time to a fire in each tract (the columns) if that tract is served by a station in a given tract (the rows). The bottom row gives the forecasted average number of fires that will occur in each of the tracts per day.

Assigned Station Located in Tract	Response Times (in minutes) Fire in Tract
	1	2	3	4	5
1	8	10	27	20	12
2	21	3	15	11	28
3	14	25	7	18	11
4	25	10	22	2	13
5	12	24	13	12	6
Average frequency of fires	3 per day	1 per day	2 per day	1 per day	2 per day

a) (10 pts) Formulate an integer programming model for this problem.

b) (10 pts) The management of Cafetown municipality now has decided that the decision on the locations of the fire stations should be based mainly on costs. The cost of locating a fire station in a tract is $150,000 for tract 1, $420,000 for tract 2, $550,000 for tract 3, $490,000 for tract 4, and $650,000 for tract 5. Management's objective now is the following: Determine which tracts should receive a station to minimize the total cost of stations while ensuring that each tract has at least one station close enough to respond to a fire in at most 16 minutes (on the average). In contrast to the original problem, note that the total number of fire stations is no longer fixed. Formulate an integer programming model for this problem.

c) (4 pts) Specify the category of problem you formulated in part (b). (i.e. fixed charge problem, traveling salesman problem etc.)

(PLEASE DO NOT USE EXCEL, SHOW YOUR INTEGER PROGRAMMING AND ANSWER PART A,B AND C)