22 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 Figure 31. 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; and town 4, 25 fires. The county wants to build the 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 a 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. (Hint: If the fire station is to be located at the point (x, y) and there is a town at the point

(a, b), define variables

e, w, n, s (east, west, north, south) that satisfy the equations x - a = w - e and y - b = n - s.

It should now be easy to obtain the correct LP formulation.)