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First-LP-example_2010

# First-LP-example_2010 - Note this material was developed by...

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Note: this material was developed by Prof. Endre Boros, Director of the Operations Research Center, RUTCOR, for a guest lecture in 2008. An example for a linear programming problem Description Giapetto’s woodcarving shop manufactures two types of wooden toys: sol- diers and trains . A soldier sells for \$27, and costs in materials and labor \$24. A train sells for \$21 and costs in material and labor \$19. The manufacturing process consists of two main operations: carpentry and finishing . A soldier requires 2 hours of finishing and 1 hour of carpentry , while a train requires 1-1 hours of each. Each week Giapetto has ample raw material, but has some limitations in work force, namely he can only have 80 hours of carpentry and 100 hours of finishing done. Furthermore, demand for trains is unlimited, however only 40 soldiers can be sold, weekly. How many soldiers and trains should Giapetto planning on weekly, so that he meets these limitations , and gains the maximum profit ? Formulation of a mathematical model Decision variables : In order to answer Giapetto’s quastion, we need to tell him only two numbers: the number of soldiers and the number of trains he has to produce weekly. Let us denote by x 1 = the number of soldiers produced each week x 2 = the number of trains produced each week We do not know in advance these numbers, but will determine them via solving a mathematical problem. Objective function : Giapetto has a clear objective, which is to increase his profit as mush as possible. Let us denote his profit by z .

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