### Optimum location of a central storage facility

## by Kamilah Owens

Submitted : Spring 2012

The purpose of this project was to find the optimum location of a central storage facility with three customers located at three different locations. The locations of the customers were located at (X_{1}, Y_{1}), (X_{2, }Y_{2}), (X_{3}, Y_{3}). The optimum location (X,Y) is based on the cost function being minimized (Eq1). Given the values of (X_{1}, Y_{1}), (X_{2, }Y_{2}), (X_{3}, Y_{3}) = (-5,0), (4,6), (10, -4), I had to minimize the cost function in two different cases (Eq2, Eq3) in order to minimize the distance. I took the first order partial derivative of Eq4 and applied the distance formula to (L_{1}, L_{2}, L_{3}). This gave me two equations (Eq8, Eq9), in which I needed to set equal to zero in order to find my critical points for (x,y). I used a program called Mathematica to solve these equations. This gave me a result of C = 21.569 for Eq2 and C= 31.8046 for Eq3.

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