Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.