tanotes8 - Q2 [10 marks]: Generally well done. Q3 [10...

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CO 350 Linear Optimization TA’s comments for Assignment 8 Q1 [10 marks]: 1. Some students assumed that the basic solution corresponding to B in the new LP is given by x B + ±d , but did not prove this. See the solution for the details of how to prove it. 2. Some students only showed that B is feasible in the new LP, not optimal. Pay more attention to what the exercise asks you to do. 3. To prove optimality of B in the new LP, the easiest way is to use the dual solution: changing b does not change the feasible region of the dual, so the basic dual solution remains feasible. Many students did not consider the basic dual solution. Others did, but did not explain why the dual solution remains feasible. You should be more careful and justify everything , every statement.
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Unformatted text preview: Q2 [10 marks]: Generally well done. Q3 [10 marks]: Generally well done. Q4 [10 marks]: The easiest answer is in the solution: the feasible region of the new LP must be a subset of the feasible region of the original LP, so its optimal value cannot increase. Some students tried to use duality but didn’t use it properly. A proper use of duality would go like this. Let y be the basic dual solution associated with B . Add one component to y with value zero, corresponding to the new constraint, and call the resulting vector y . Then x * and y are both feasible in their respective LPs and have the same objective value. Thus, x * is optimal for the new LP. Q5 [20 marks; (4 marks on each part)]: Generally well done. 1...
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This note was uploaded on 05/28/2011 for the course CO 350 taught by Professor S.furino,b.guenin during the Winter '07 term at Waterloo.

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