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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 Winter '07
 S.Furino,B.Guenin
 Optimization, AP, TA

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