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CO350 Assignment 4
–
Wing Man Fok
20300650
,
June 11 2010
:

Instructor Mathieu Guay Paquet
1a
:
Consider the linear program
( )
P max 2 x1
2 x2
3 x3
3 x5
. .
&&&
s t
x1
x2
2 x3
&
2 x5
0
x2
x3
2 x5
1
x1
x2
x4
4 x5
5
x1
x2
x3
x4
x5
0
={ , , }
The tableau associated with the basis B
1 2 4 is
&&
z
3 x3
x5
4
x1
x3
1
x2
x3
2 x5
1
x4
2 x5
3
1b
= , , , ,
.
The basic solution is x 1 1 0 3 0T and its objective value is 4 x is feasible as
≥ .
x 0
1c
=

=( , , )
The basic dual solution y ABT 1cB
2 4 0
= , , , ,
≥ ,
.
Since ATy 2 2 0 0 4T c y is feasible
2a
:
The tableau associated with the basis B is
&&
z
2 x4
x5
0
x1
x4
x5
1
x2
x4
3 x5
3
x3
x4
x5
2
= ,
= .
=
= + ,  ,  , ,
Let x4 t x5 0 zt 2t and xt 1 t 3 t 2 t t 0T
≥ ⇒ ≤ .
=
= , , , ,
.
Note xt 0 t 2 Let x x2 3 1 0 2 0T
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This note was uploaded on 05/28/2011 for the course CO 350 taught by Professor S.furino,b.guenin during the Fall '07 term at Waterloo.
 Fall '07
 S.Furino,B.Guenin

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