primal_dual_rel_ex - Example of primal-dual relationship...

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Example of primal-dual relationship Consider the BM company problem. The optimal solution is x 1 * = 2, x 2 * = 0, and Z* = 6. The dual problem is An optimal solution is y 1 * = 0, y 2 * = 3/2, and w * = 6. x 1 x 2 6 1 3/4 Z = 4 c O 2 Z * = 6 12 1 2 1 1 2 2 (P) max Z 3 4 subject to 3 6 2 4 4 0, 0 xx x x y x x y   y 1 1 3/2 c O 1 2 1 1 2 2 (D) min w 6 4 subject to 3 2 3 4 4 0, 0 yy y y x y y x y 2 4 1 3/2
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To see weak duality in action, pick two feasible solutions of (P) and (D). e.g., o x 0 = (0, 1) and y 0 =(4, 0) Z( x 0 ) = 4 < w(y 0 ) = 24, o x 1 = (0, 1), y 1 =(3/2, 1) Z( x 1 ) = 4 < w(y 1 ) = 13, o x 2 = (1/2, 3/4), y 2 =(3/2, 1) Z( x 2 ) = 9/2 < w(y 2 ) = 13, o and much more. Try it! To see strong duality, note that in this case both (P) and (D) have optimal solutions.
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This note was uploaded on 12/23/2010 for the course ENMG 500 taught by Professor Drbacelmaddah during the Fall '09 term at American University of Beirut.

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primal_dual_rel_ex - Example of primal-dual relationship...

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