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# mt.marking.comments - C&O 350 Linear Optimization Winter...

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C&O 350 Linear Optimization – Winter 2010 – Marking Comments for Midterm Exam Q1: (a) Some students forgot the third constraint, - y 1 + 2 y 2 0. (b) Some students tried to use the substitution x 3 = 6 - 2 x 2 , or something similar. Since neither x 2 , x 3 are free variables, this almost certainly led to other errors. Q2: (a) Very well done. (b) Ditto. (c) Again, the majority of students answered this question correctly. Some did not read the question carefully and only gave one pair of leaving/entering variables. Many had the correct pairs but also included some extra incorrect ones, and lost points for that. (d) This was again well done. Students who were incorrect in (c) and (d) in a consistent way (i.e. their solution in (d) would have been correct if that in (c) was) were given the points in (d). Also, about 20 students claimed that 2+ 1 2 = 3 2 . This, and many other small arithmetic errors, were not penalized. Q3: (a) This question was well done. Some students wrote that the algorithm stops when all c j 0 instead of c j 0. (b) Many students assumed that y * was an optimal solution to the dual. This is wrong. The solution y * was a feasible solution to the dual but it might be non optimal. The students that claimed α = 6 got zero marks. Q4: Note: Parts a and b were marked generously. Many students got 1 out of 2 marks for incomplete or only partially correct answers. Many such answers did not at all suggest that the students had understood what a basis/basic solution is about. If a similar question is repeated on the final exam, 0 out of 2 will be the default mark for incomplete or partially correct definitions.

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