IE 534 Linear Programming Homework
6
•
Assigned on Friday 10/09/2015.
•
Due by 10:00 AM (CST) on Monday 10/19/2015.
•
Homework submitted at 10:01 AM or later will not be accepted.
•
Submission can be in hard copy or by email as a single pdf document to
lzw
[email protected]
1. (10 points) The set of partitions of
{
1
,
2
, ..., n
+
m}
can be divided into the
following regions.
A+B+C+D:
All possible
partitions
B+C+D:
Basic partitions
C+D:
Feasible basic
partitions
D:
Optimal basic
partitions
Consider the following LP.
Transform it into
max
{c
T
max
x
1
+ 2
x
2
+ 3
x
3
s
.
t
.
x
1
−
3
x
3
≤
0
7
x
1
+ 2
x
2
+ 5
x
3
≤
1
x
1
,
x
2
, x
3
≥
0
.
x
:
A
m
×
(
n
+
m
)
x
=
b
m
×
1
, x
(
n
+
m
)
×
1
≥
0
}
, and answer these
question
s.
(
n
+
m
)
×
1
(a)
How many partitions (
B, N
) of
{
1
,
2
, ...n
+
m}
are there with
|B|
=
m, |N |
=
n
?
1

If m = 2 and n = 3, then (m + n) *n = (3 + 2) * 2 = 5 * 2 = 10 total
partitions.
(b) List all these partition. For each partition, identify
one
specific region (e.g., B
is one
region, B + C is not) that it belongs to. If a partition is basic, also give
the basic solution
and its objective value.
Partition 1
>>dictionary
dict =
' '
' '
'w4'
'x3'
'w5'
'zeta'
[
1]
[
6]
[-20]
[
-1]
'x1'
[
0]
[
-1]
[
3]
[
0]
'x2'
[0.5000]
[3.5000]
[-13]
[-0.5000]
Partition 2
>> dictionary
dict =
' '
' '
'x2'
'w4'
'w5'
'zeta'
[0.2308]
[ 1.5385]
[ 0.6154]
[-0.2308]
'x1'
[0.1154]
[-0.2308]
[-0.1923]
[-0.1154]
'x3'
[0.0385]
[-0.0769]
[ 0.2692]
[-0.0385]
Partition 3

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