Problem:
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
|
Required:
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.
Solve the given numerical problem and illustrate step by step calculation.