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# GE330_lect9 - Lecture 9 Duality and Post-Optimal Analysis...

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Lecture 9: Duality and Post-Optimal Analysis February 19, 2009

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Lecture 9 Topic Outline Dual of an LP Problem Primal-Dual Relationship Economic Interpretation of Duality Post-Optimal Analysis Chapters 4.1, 4.2, 4.3, and 4.5. GE330 1
Lecture 9 Today: LP Duality Dual of an LP Problem Primal-Dual Relationship Review for Midterm I GE330 2

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Lecture 9 LP Dual The original LP is referred to as primal The dual is another LP associated with the given LP It is defined directly and systematically An LP and its dual are closely related: an optimal solution of one automatically provides information about an optimal solution of the other one Rules of the dual LP formulation: consider LP in a standard form To each equation assign a variable The objective coefficients in the dual are given by the right-hand side of the primal (system of equations): if primal objective is “max” the dual objective is “min” (and v.v) To each primal variable assign a constraint The column coefficients of a primal variable define the row coefficients of a dual constraint, while the objective cost of the variable defines the right-hand side of the constraint in the dual GE330 3
Lecture 9 Rules for Standard Form: MAX Standard LP (primal) problem maximize z = c 1 x 1 + c 2 x 2 + · · · + c n x n subject to a 11 x 1 + a 12 x 2 + · · · + a 1 n x n = b 1 ←- y 1 a 21 x 1 + a 22 x 2 + · · · + a 2 n x n = b 2 ←- y 2 .

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