Duality Theorem Handout

Duality Theorem Handout - Duality Theorem Handout...

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Unformatted text preview: Duality Theorem Handout Agenda: 1) 2) 3) 4) 5) 6) Introducing two versions of Duality Theorem Farkas’ Lemma Another Important Lemma Proof of Duality Theorem Application of Duality Theorem – Min ­Max Theorem Example of Min ­Max Theorem  ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1) 2) 3) 4) 5) 6) Example of Duality Theorem: The manager of the ATV plant seeks the mix of activities that maximizes the rate at which contribution is earned, measured in dollars per week. The decision variables are the rates at which to produce the three types of vehicles, which are given the names: S = the rate of production of Standard model vehicles (number per week) F = the rate of production of Fancy model vehicles (number per week) L = the rate of production of Luxury model vehicles (number per week). Label of the shadow prices – E for Engine shop, B for Body shop, SF for Standard Finishing shop, and so forth. The decision variables in this linear program are the prices that you will offer. By agreement, you must offer five prices, one per shop. These prices are labeled: E = the price ($/hour) you offer for each unit of Engine shop capacity. B = the price ($/hour) you offer for each unit of Body shop capacity. SF = the price ($/hour) you offer for each unit of Standard Finishing shop capacity. FF = the price ($/hour) you offer for each unit of Fancy Finishing shop capacity. LF = the price ($/hour) you offer for each unit of Luxury Finishing shop capacity. The solved optimal value is 50,400 $/wk, and the shadow prices of its three constraints are S = 20, F = 30, L = 0. Program 1 and Program 3 have the same optimal value, and the shadow prices of each form an optimal solution to the other. ...
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This note was uploaded on 08/12/2011 for the course MATH 480 taught by Professor Staff during the Spring '11 term at Yale.

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