## Simplex Algorithm and How Dating Web Sites Match Singles

Mathematical Background: The simplex method was created by George Dantzig (1914-2005) who was Professor Emeritus of Transportation Sciences and Professor of Operations Research and Computer Science at Stanford University. George Dantzig created the simplex method as an algorithm for solving a system of linear equations. The algorithm is used in linear programming to find optimum solutions to these equations. The equations typically consist of one objective function which you are trying to minimize (i.e. cost) or the dual problem which would consist of an equation your are trying to maximize(i.e. profit). In addititon to the objective function you will have some sort of constraints which will limit your optimum solution. These constraints could be in the form of storage capacity, capital budgets, time constraints, labor expenses, substitutability of inputs and a host of other factors can play a part in defining the set of constraints. The original applications to the simplex method were to linear programming. Linear programming was used during WWII was as a way of minimizing cost to the army and increase losses to the enemy through superior planning and utilization of resources. Examples of the uses of the simplex method and linear programming include the transportation problem where the algorithm minimizes the cost of shipping between n number of warehouses and m number of destinations. The diet problem is another application where the nutritional needs of an army are taken into account as we try and minimize...

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