Unformatted text preview: concluding the that the LP is unbounded. This misses the point of the question, which calls for an observation “from tableau T 2 .” For the proof of unboundedness, there should be two main ingredients: 1. Giving a family of solutions x ( t ) that is feasible for every t ≥ 0; 2. Showing that the objective value of x ( t ) tends to ∞ as t does. Many students only did (1), which is not enough, since it’s possible for an LP that is not unbounded to have an unbounded feasible region. Q4: Mistakes: • forgetting that the reduced cost ¯ c j of a nonbasic variable x j appears with a negative sign in the zrow; Q7: Mistakes: • not checking that the solution x * found in item (b) is feasible; • assuming that the “or” in the complementary slackness conditions is exclusive. For instance, y 2 + 2 y 4 > 5 implies that x 2 = 0, but y 2 + 2 y 4 = 5 does not imply that x 2 > 0. 1...
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 Fall '07
 S.Furino,B.Guenin
 Linear Programming, Optimization, TA, Simplex algorithm, objective value

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