Question: Question 4: Monroe County is trying to determine where to place the county fire station. The locations of the county's four major towns are given in the figure shown.

Town 1 is at (10, 20); Town 2 is at (60, 20); Town 3 is at (40, 30); Town 4 is at (80, 60). Town 1 averages 20 fires per year; Town 2, 30 fires; Town 3 40 fires; Town 4 25 fires. The county wants to build a fire station in a location that minimizes the average distance that a fire engine must travel to respond to a fire. Since most roads run in either an east-west or north-south direction, we assume that the fire engine can only do the same. Thus, if the fire station were located at (30, 40) and a fire occurred at Town 4, the fire engine would have to travel (80-30) + (60-40) = 70 miles to the fire. Use linear programming to determine where the fire station should be located.

Please enter the horizontal coordinate of the location that you propose.