a3 - CO350 Assignment 3 Wing Man Fok 20300650 May 28, 2010...

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CO350 Assignment 3 Wing Man Fok 20300650 , May 28 2010 : - Instructor Mathieu Guay Paquet 1. The dual problem is . . min 12 y1 22 y2 8 y3s t ≥ &&- 12 y1 7 y2 3 y3 2 y1 y3 2 2 y1 3 y2 y3 1 y1 4 y2 y3 2 . . The C S conditions are *= *= *&& *&&=- x1 0 or 12 y1 7 y2 3 y3 2 x2 0 or y1 y3 *= *= 2 x3 0 or 2 y1 3 y2 y3 1 x4 0 or y1 4 y2 y3 2 . Consider the proposed solutions for the primal problem ( ) i = , , , . . . . x 1 1 1 3T is feasible Suppose that y satisfies the C S conditions with x > . , Notice that x 0 Therefore && 12 y1 7 y2 3 y3 2 y1 y3 2 2 y1 3 y2 y3 1 y1 4 y2 y3 2 , . The system of equations has no solution so x is not optimal ( ) ii = , , , . . . . x 0 1 6 1T is feasible Suppose that y satisfies the C S conditions with x > = , , . , Notice that xk 0 for k 2 3 4 Therefore && &&= & &- y1 y3 2 2 y1 3 y2 y3 1 y11 4 y2 y3 2
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a3 - CO350 Assignment 3 Wing Man Fok 20300650 May 28, 2010...

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