CO 350 Linear Optimization TA’s comments for Assignment 4 General: Many students are still making arithmetic mistakes. Please double check all your calculations before you hand in your assignment. Q1 [(a) 4 marks; (b) 2 marks; (c) 4 marks]: 1. In part (a), some students forgot to apply the row operations to the z-row. If you are still having problems with how the simplex method works, you are in serious trouble. Fix that. 2. In part (c), many of you did not justify why y is feasible. The reason is that ¯ c ≤ 0 (look at the z-row of the tableau). Recall that the simplex method terminates with an optimal solution precisely when ¯ c ≤ 0. Since ¯ c = c-A T y , where y is the basic dual solution, the condition ¯ c ≤0 is equivalent to A T y ≥ c , i.e., y is feasible in the dual. 3. Still in part (c), some of you did not ﬁnd y properly because the following system was used: A B y = c B . Note that the correct system to solve is ( A B ) T y = c B . Q2 [(a) 5 marks; (b) 5 marks]:
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