sol8 - CO350 Homework 8 Solutions Winter 2007 Due Friday...

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CO350 Homework 8 Solutions– Winter 2007 Due: Friday, March 17, 2007. Hand in at the start of class. 1. The Auxiliary Problem of Phase 1 (a) The auxiliary problem is bounded above by 0. This tableau has an objective value of 1. (b) The basic solution corresponding to the tableau has an x 2 value of 0. But since w + x 5 + x 6 = 0 the w -row of the tableau implies that x 2 = 2 = 0. (c) The auxiliary problem is bounded above by 0. If x 1 enters, the problem is unbounded. (d) Since w + x 5 + x 6 = 0 and since the given w -row is a linear combination of w + x 5 + x 6 = 0 with the other two rows, it must mean that x 1 = 0 can be written as a linear combination of the other two rows. This is clearly not possible. 2. Basic Solutions and Degeneracy Consider any basic feasible solution x * s * of (Q). x * is a feasible solution of (P). x * j = 0 satisfies the non-negativity constraint x * j 0 with equality. If the slack variable s * i = 0 in the equation A i x * + s * i = 0 in (Q) then the constraint A i x * 0 is satisfied with equality in (P).
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