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# Revised Simplex Method Notes | EduRev

## : Revised Simplex Method Notes | EduRev

``` Page 1

Revised Simplex Method 09/23/04 page 1 of  22

(includes both Phases I  &  II)

Dept of Mechanical & Industrial Engineering
The  University of Iowa
Page 2

Revised Simplex Method 09/23/04 page 1 of  22

(includes both Phases I  &  II)

Dept of Mechanical & Industrial Engineering
The  University of Iowa
Revised Simplex Method 09/23/04 page 2 of  22

1 2 34 56
Minimize z=3x 5 4 7 5 4 xx x x x ++ + + +
subject to

12 4 6
13 4 5 6
23 4 5
2310
33212
42 3 15
xx x x
xx x x x
xx x x
-+ + =
?
?
+- + + =
?
?
++ + =
?

and  0   1, 6
j
x j =?= …

Because of the lack of a slack variable in each constraint, we must use
Phase I to find an initial feasible basis.

9
, X
10
, X
11
(artificial variables), and
a Phase I objective of minimizing the sum of these three variables.

Page 3

Revised Simplex Method 09/23/04 page 1 of  22

(includes both Phases I  &  II)

Dept of Mechanical & Industrial Engineering
The  University of Iowa
Revised Simplex Method 09/23/04 page 2 of  22

1 2 34 56
Minimize z=3x 5 4 7 5 4 xx x x x ++ + + +
subject to

12 4 6
13 4 5 6
23 4 5
2310
33212
42 3 15
xx x x
xx x x x
xx x x
-+ + =
?
?
+- + + =
?
?
++ + =
?

and  0   1, 6
j
x j =?= …

Because of the lack of a slack variable in each constraint, we must use
Phase I to find an initial feasible basis.

9
, X
10
, X
11
(artificial variables), and
a Phase I objective of minimizing the sum of these three variables.

Revised Simplex Method 09/23/04 page 3 of  22
Phase One

1  2 3  4 5 6  7  8 9 0 1  b
0  0 0  0 0 0  0  0 1 1 1  0    phase one objective
3  5 4  7 5 4  0  0 0 0 0  0    phase two objective
2 -1 0  1 0 3  0  0 1 0 0 10
1  0 3 -1 3 2 -1  0 0 1 0 12
0  4 2  3 1 0  0 -1 0 0 1 15

Values of basic (artificial) variables are:

i   Xi
9   10
10   12
11   15

Page 4

Revised Simplex Method 09/23/04 page 1 of  22

(includes both Phases I  &  II)

Dept of Mechanical & Industrial Engineering
The  University of Iowa
Revised Simplex Method 09/23/04 page 2 of  22

1 2 34 56
Minimize z=3x 5 4 7 5 4 xx x x x ++ + + +
subject to

12 4 6
13 4 5 6
23 4 5
2310
33212
42 3 15
xx x x
xx x x x
xx x x
-+ + =
?
?
+- + + =
?
?
++ + =
?

and  0   1, 6
j
x j =?= …

Because of the lack of a slack variable in each constraint, we must use
Phase I to find an initial feasible basis.

9
, X
10
, X
11
(artificial variables), and
a Phase I objective of minimizing the sum of these three variables.

Revised Simplex Method 09/23/04 page 3 of  22
Phase One

1  2 3  4 5 6  7  8 9 0 1  b
0  0 0  0 0 0  0  0 1 1 1  0    phase one objective
3  5 4  7 5 4  0  0 0 0 0  0    phase two objective
2 -1 0  1 0 3  0  0 1 0 0 10
1  0 3 -1 3 2 -1  0 0 1 0 12
0  4 2  3 1 0  0 -1 0 0 1 15

Values of basic (artificial) variables are:

i   Xi
9   10
10   12
11   15

Revised Simplex Method 09/23/04 page 4 of  22
Page 5

Revised Simplex Method 09/23/04 page 1 of  22

(includes both Phases I  &  II)

Dept of Mechanical & Industrial Engineering
The  University of Iowa
Revised Simplex Method 09/23/04 page 2 of  22

1 2 34 56
Minimize z=3x 5 4 7 5 4 xx x x x ++ + + +
subject to

12 4 6
13 4 5 6
23 4 5
2310
33212
42 3 15
xx x x
xx x x x
xx x x
-+ + =
?
?
+- + + =
?
?
++ + =
?

and  0   1, 6
j
x j =?= …

Because of the lack of a slack variable in each constraint, we must use
Phase I to find an initial feasible basis.

9
, X
10
, X
11
(artificial variables), and
a Phase I objective of minimizing the sum of these three variables.

Revised Simplex Method 09/23/04 page 3 of  22
Phase One

1  2 3  4 5 6  7  8 9 0 1  b
0  0 0  0 0 0  0  0 1 1 1  0    phase one objective
3  5 4  7 5 4  0  0 0 0 0  0    phase two objective
2 -1 0  1 0 3  0  0 1 0 0 10
1  0 3 -1 3 2 -1  0 0 1 0 12
0  4 2  3 1 0  0 -1 0 0 1 15

Values of basic (artificial) variables are:

i   Xi
9   10
10   12
11   15

Revised Simplex Method 09/23/04 page 4 of  22  Revised Simplex Method 09/23/04 page 5 of  22
Iteration 1

Current partition: (B = basis, N = non-basis)

B= {9 10 11}, N= {1 2 3 4 5 6 7 8}

Basis inverse is

1 0 0
0 1 0
0 0 1

Simplex multipliers (dual solution):

i    p
1    1
2    1
3    1

() []
1
10 0
1,1,1 0 1 0 [ 1 ,1 ,1]
00 1
B
B
cA
-
??
??
?p= = =
??
??
? ?
```
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