Set_4_duality

# Set_4_duality - Dr Maddah ENMG 500 Engineering Management I...

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1 Dr. Maddah ENMG 500 Engineering Management I 11/1/06 Duality Overview Every LP problem has a twin problem associated with it. One problem is known as the primal , and the other as the dual . The properties of the two problems are closely related, and they have the same optimal solution. The reasons we care about the dual of an LP are (i) Utilizing the dual solution, we can do a sensitivity analysis of the LP. That is, we assess the effect of changing the problem parameters on the optimal solution; 1 (ii) It may be easier to solve the dual first and then deduce the primal solution than to solve the primal directly. Formulation of the dual problem If the primal is a max (min) problem then the dual is a min (max) problem. To each primal constraint corresponds a dual variable. The objective function coefficients of the dual are the RHS values of the primal. The sign of a dual variable is based on the type of the corresponding primal constraint (“≤”, “≥”, or “=”) as indicated in Table 1. To each primal variable corresponds a dual constraint. The type of a dual constraint is defined based on the sign of the corresponding primal variable as indicated in Table 1.

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Set_4_duality - Dr Maddah ENMG 500 Engineering Management I...

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