CO350 Assignment 5
–
Wing Man Fok
20300650
,
June 18 2010
:

Instructor Mathieu Guay Paquet
1
.
Suppose xj is the leaving variable during one iteration of simplex method
.
≥ .
Let xi denote the entering variable in that particular iteration Note that ci 0
,
> .
Since xj is the leaving variable aji 0 When pivoting the tableau for the next
,


.
(
iteration we add ciaji times the xj row from the z row It follows that cj in the
)=
<
new tableau
ciaji 0
,
.
Hence xj cannot be an entering variable in the next iteration
2
=
,
=
,
= , , ,
A 21100101 b 62 c 3 1 1 1T
Iteration 1
= , .
*= , , ,
B 2 3 x
0 2 4 0T
=

=

=

=
y AB TcB 1110 111 011 111 10
= 
= , , ,
 , , ,
= , , ,
c c yTA 3 1 1 1T 2 1 1 0T 1 0 0 1T
.
x1 enters
=

=

=
A1 AB 1A1 011 120 02
=
,
=
t min 42 2
.
x3 leaves
Iteration 2
={ , } , *= , , ,
B
1 2
x
2 2 0 0T
=

=

=

=

y AB TcB 2101 T31 1210 1231 123 1
= 
= , , ,

, , ,
=
, , ,
c c yTA 3 1 1 1T 126 2 3 1T 120 0 1 1T
.
x4 enters
=

= 

=

A4 AB 1A4 1 102 101 12 12
=
,