CO 227  Homework assignment 3
Fall ‘10
Page 1
CO 227  Fall ‘10
Homework assignment #3:
(Due at Monday, Oct 18th, at 4pm)
Instructions:
•
Please show all your work and justify your answers. Answers without proper justification
will not be considered.
•
Please list who you collaborated with.
•
Please staple your homework and write your name and student id in pen.
•
Total value = 100 points
Question 1
 Simplex method
(100 points)
Consider the following feasible LPs. For each of them, either obtain an optimal solution by providing a
certificate of optimality or show that the LP is unbounded by providing a certificate of unboundedness.
Show all your work by rewriting the LP in canonical form at each step.
You may have several choices for variables entering/leaving the basis. However, to make
the correction easier, if there is a choice, always choose the lowest index variable. If you
do not do that, you will be penalized.
(a) (50 points)
max
z
(
x
) = (1
,
4
,

1
,
3
,
0
,
0)
x
s.t.
parenleftbigg
1

2
3
2
1
0
2

1
0

2
0
1
parenrightbigg
x
1
x
2
x
3
x
4
x
5
x
6
=
parenleftbigg
1
1
parenrightbigg
x
≥
vector
0
(1)
Start with the basis
B
=
{
5
,
6
}
.
Solution:
Choose a nonbasic variable with
c
k
>
0. Since there are several choices, we choose
x
1
to enter the basis.
Keeping
x
2
,x
3
,x
4
= 0, we have
parenleftbigg
1
2
parenrightbigg
t
+
parenleftbigg
x
5
x
6
parenrightbigg
=
parenleftbigg
1
1
parenrightbigg
So
t
=
min
i
:
A
ik
>
0
{
b
i
A
ik
}
= min
{
1
1
,
1
2
}
=
1
2
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 Spring '10
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 BMW Sports Activity Series, Canonical form, BMW X5, All wheel drive vehicles

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