Mathematical formulation of the optimization problem

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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.

 

Reference no: EM13100481

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