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Duality and Post-Optimal Analysis by amna ali

Duality and Post-Optimal Analysis by amna ali. LP Dual •. The original LP is referred to as primal • The dual is another LP associated with the given LP • It is defined systematically

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Duality and Post-Optimal Analysis by amna ali

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  1. Duality and Post-Optimal Analysisby amna ali

  2. LP Dual • • The original LP is referred to as primal • The dual is another LP associated with the given LP • It is defined systematically • An LP and its dual are closely related: an optimal solution of one provides information about an optimal solution of the other one (MC=MR)

  3. • Rules of the dual LP formulation: • consider LP in a standard form • To each equation assign a variable • The objective coeficients 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 coeficients of a primal variable define the row coeficients of a dual constraint, while the objective cost of the variable defines the right-hand side of the constraint in the dual

  4. PRIMAL: Maximize Z = 3 X1 + 2 X2 + 5 X3 Subject to: X1 + 2 X2+ X3<430 (operation 1) 3 X1 +2X3<460 (operation 2) X1 + 4 X2<420 (operation 3) DUAL : Minimize C =430y1+460y2+420y3 Subject to: y1+3y2+y3 > 3 2y1+4y3 > 2 Y1+4y2 > 5

  5. Determining Dual Optimal Solution from Optimal Simplex Table

  6. Identity matrix ½ -1/4 0 0 ½ 0 -2 1 1

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