The JLM Ambulance Service serves five rural towns, Abbeville, Benton, Clayton, Dunning and Eden. JLM wants to construct a centralized facility and garage to minimize its total annual travel mileage to those towns. The location of the five towns in terms of their graphical x and y coordinates in miles relative to the point (x,y)=(0,0) and the expected number of trips to each town are given below:

Coordinates

Town
x
y
Annual number of trips
Abbeville
20
20
75
Benton
10
35
105
Clayton
25
9
135
Dunning
32
15
60
Eden
10
8
90

Develop a mathematical formulation of the optimization problem that determines the coordinates (x,y) of the centralized facility so that the total number of miles traveled to the five towns is minimized, and solve the nonlinear optimization problem with Excel solver.