tanotes3 - concluding the that the LP is unbounded This...

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CO 350 Linear Optimization (Spring 2009) TA’s comments for Assignment 3 Q1: The 4 parts are worth 3, 3, 8, and 6 points respectively. A remarkable number of students failed to follow the directions of the question. Several students blindly ran the simplex algorithm on the given tableau (and did not even attempt a) and b)), while a few others did not give the optimal solution and/or its objective value in d). A few students made an error while running the simplex method in c), and end up losing a big portion of the marks. Keep in mind that, if after an iteration, you end up with an infea- sible solution, or an objective value that’s lower than before, then you must have screwed up somewhere. Q2: 3 points for observing from the given tableau that x 4 can be increased indefinitely, and 7 points for giving the “proof of unboundedness.” Some students performed 2 or even 3 iterations of the simplex method on the given tableau before
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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 z-row; 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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