Homework 8

Homework 8 - CO350 Homework 8 Winter 2007 Due: Friday,...

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CO350 Homework 8 – Winter 2007 Due: Friday, March 16, 2007. Hand in at the start of class. 1. The Auxiliary Problem of Phase 1 Each of the following tableaus is an invalid tableau that cannot arise when the simplex algo- rithm is run in Phase 1 on an auxiliary problem. For each tableau, give a reason that proves that the tableau is invalid. In all cases, the auxiliary problem has objective function w = - x 5 - x 6 , where x 5 and x 6 are the artiﬁcial variables, which have been retained as part of the tableau. Each tableau corresponds to a diﬀerent auxiliary problem. (a) w + x 1 + x 2 + x 4 + x 5 = 1 2 x 1 - x 2 + x 3 - x 4 + 3 x 5 = 2 - x 1 + x 2 + 2 x 4 - x 5 + x 6 = 3 (b) w - x 2 + x 5 + x 6 = - 2 x 1 - x 2 - 2 x 3 - x 5 - x 6 = 2 + x 2 - x 3 + x 4 + 2 x 5 - x 6 = 3 (c) w - x 1 + x 3 + 2 x 4 + 4 x 6 = - 1 - x 1 + x 2 + 3 x 3 + x 4 + 2 x 6 = 4 - 3 x 1 - x 3 - x 4 + x 5 - x 6 = 1 (d) w + x 1 + x 5 + x 6 = 0 2 x 1 + x 2 - x 3 - x 5 + 2 x 6 = 1 x 1 + x 3 + x 4 - x 6 = 2 2. Basic Solutions and Degeneracy Let

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This note was uploaded on 07/28/2009 for the course CO 350 taught by Professor S.furino,b.guenin during the Winter '07 term at Waterloo.

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Homework 8 - CO350 Homework 8 Winter 2007 Due: Friday,...

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