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Formulate a Model to Determine Location in the (x,y) Plane

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Five train stations located in the (x,y) plane have the coordinates (ai, bi) given by
(a1, b1) = (5, 0)
(a2, b2) = (0, 10)
(a3, b3) = (10, 10)
(a4, b4) = (50, 50)
(a5, b5) = (-10, 50)

It is desired to connect all of the stations to a single location "hub" using the minimum total amount of track. Each track segment will be placed in a straight line from the station to the "hub".
a) Formulate a mathematical program that can be used to determine where the "hub" should be located in the plane. Clearly define your decision variables, objective and constraints
b) Implement your formulation in Excel and use Solver to find the optimal answer. Include a snapshot of your answer.

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Solution Summary

The answer shows the formulation of a model to determine the location on the (x, y) plane.

Solution Preview

We let (c,d) be the co-ordinate of the hub to which all the stations will be connected. From the question, you will observe that a requirement is that the central hub be connected to all the stations in a straight line. It therefore means that the central location can be at any ...

Solution provided by:
Chidi Ngene, M. Sc.
Education
  • B. Sc., University of Nigeria
  • M. Sc., London South Bank University
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