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Unformatted text preview: 3 = 1 x 1 + x 3 = 0 x 2 + x 3 = 1 After one pivot, this tableau becomes optimal, so there are no ties for the choice of leaving variable during the running of simplex, and yet the basis B = { 1 , 2 } is degenerate. Q2 [(a) 5 marks; (b) 5 marks]: This question was very poorly done. For instance, many students didnt realize that they could use the result from part (a) to prove part (b). Please see the solution. Q3 [10 marks]: Many students didnt realize that they could not apply Strong Duality Theorem in SEF to the dual problem min { b T y : A T y c } . Note that, while the primal LP is in SEF, this LP (the dual) is not in SEF. Thus, to use the Strong Duality Theorem for SEF for this LP, you rst had to transform it into SEF, and form its dual, then translate the conclusion back into the notation of the original problem max { c T x : Ax = b, x } . Q4 [(a) 5 marks; (b) 5 marks]: Generally okay, except for arithmetic mistakes. 1...
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 Winter '07
 S.Furino,B.Guenin

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