CO350 L
INEAR
P
ROGRAMMING
 A
SSIGNMENT
8
Due Date:
Friday July 16 at 2 PM in assignment drop box 2, in front of MC4066.
Please make sure that your name and student number, the course number, and the name of your instructor
are
clearly
written on the front of your assignment, and that all pages are securely stapled. You may discuss
the assignment questions with other students, but you must write your solutions up independently, and all
submitted work must be your own.
Exercise 1.
Consider the linear program
(
P
)
max
{
c
T
x
:
Ax
=
b, x
≥
0
}
where
A
∈
R
m
×
n
,
c
∈
R
n
and
b
∈
R
m
. Let
B
be an optimal basis for
(
P
)
, let
x
be the associated basic
solution, let
∈
R
and let
d
be the
i
th
column of
(
A
B
)

1
. Show that if we replace
b
i
by
b
i
+
and we have
x
B
+
d
≥
0
then
B
remains an optimal basis.
Exercise 2.
Consider the linear program max
{
c
T
x
:
Ax
=
b, x
≥
0
}
where
A
=

3
1
0

1
0
1
2
0
0
1
1

2
7
0
1
2
0

3
, b
=

4
3
8
,
and
c
= [

7
,
0
,
0
,

2
,
0
,

1]
T
.
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 Fall '07
 S.Furino,B.Guenin
 Operations Research, Linear Programming, Optimization, Simplex algorithm, linear program

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