Q1. A county consists essentially of nine small towns. County officials are trying to decide where they should build a modern hospital to serve all of the countys residents. In choosing where they should build the new hospital, county officials would like to maximize the total number of county residents who live within 15 miles of the town in which the hospital would be located. The problem needs to be set as a linear program.

Table:1

Distance (in miles) from each town to each other town

Town 1 Town 2 Town 3 Town 4 Town 5 Town 6 Town 7 Town 8 Town 9

Town 1	0	20	30	35	18	15	20	22	10
Town 2	20	0	15	13	12	21	10	10	17
Town 3	30	15	0	6	19	13	22	5	13
Town 4	35	13	6	0	8	18	4	17	21
Town 5	18	12	19	8	0	6	14	12	14
Town 6	15	21	13	18	6	0	11	21	8
Town 7	20	10	22	4	14	11	0	5	27
Town 8	22	10	5	17	12	21	5	0	6
Town 9	10	17	13	21	14	8	27	6	0

Table:2 Towns	Number of residents
Town 1	1526
Town 2	2317
Town 3	2598
Town 4	3012
Town 5	2254
Town 6	1578
Town 7	1166
Town 8	2178
Town 9	614