9 Metodo Simplex Mayor Maximizacion

Diapositiva 1

METODO SIMPLEXCaso en que las restricciones sondel tipo >Luis Medina AquinoPROBLEMAFORMA CANONICAMaximizar Z = 2 X1 + 4 X2 + 3 X3Sujeto a:

- X1+ X2 + 2 X3 9

6 X1 2 X2 + 2 X3 = 6

2 X1 + 2 X2 + X3 4

X1, X2, X3 0

PROBLEMAFORMA CANONICAMaximizar Z = 2 X1 + 4 X2 + 3 X3Sujeto a:

- X1+ X2 + 2 X3 9 (S1)

6 X1 2 X2 + 2 X3 = 6 (a1)

2 X1 + 2 X2 + X3 4 (-S2, a2) X1, X2, X3 0

PROBLEMAMaximizar Z = 2 X1 + 4 X2 + 3 X3Sujeto a:

- 1 X1 + 1 X2 + 2 X3 < 9 (S1)

6 X1 - 2 X2 + 2 X3 = 6 (a1)

2 X1 + 2 X2 + 1 X3 > 4 (-S2, a2)

X1, X2, X3 0

FORMA ESTANDARMaximizar Z = 2 X1 + 4 X2 + 3 X3 + 0 S1 + 0 S2 - M a1 - M a2Sujeto a:

-1 X1 + 1 X2 + 2 X3 + 1 S1 + 0 S2 + 0 a1 + 0 a2 = 9

6 X1 - 2 X2 + 2 X3 + 0 S1 + 0 S2 + 1 a1 + 0 a2 = 6

2 X1 + 2 X2 + 1 X3 + 0 S1 1 S2 + 0 a1 + 1 a2 = 4

X1, X2, X3, S1, S2, a1, a2 0

Cj-Zj < 0Maximizar Z = 2 X1 + 4 X2 + 3 X3 + 0 S1 + 0 S2 - M a1 - M a2Sujeto a:-1 X1 + 1 X2 + 2 X3 + 1 S1 + 0 S2 + 0 a1 + 0 a2 = 9

6 X1 - 2 X2 + 2 X3 + 0 S1 + 0 S2 + 1 a1 + 0 a2 = 6

2 X1 + 2 X2 + 1 X3 + 0 S1 1 S2 + 0 a1 + 1 a2 = 4

X1, X2, X3, S1, S2, a1, a2 0

R01R02R03Cj-Zj < 0

R01R02R03Cj-Zj < 0

R01R02R03Cj-Zj < 0

R01R02R03Cj-Zj < 0Columna pivote

R01R02R03

No6/6 = 1

4/2 = 2

Cj-Zj < 0Columna pivote

R01R02R03

No6/6 = 1 4/2 = 2


R01R02R03

Fila

pivote


R01R02R03Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 001 0 1 11 2

1= R

+ 1 R

+ R1

1101R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 001 0 1 11 2

1= R

+ 1 R

+ R1


Cj-Zj < 0

11R1213Cj-Zj < 001 0 1 11 2

1= R

+ 1 R

+ R1

R101R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 001 0 1 11 2

1= R

+ 1 R

+ R1


Cj-Zj < 0

11R1213Cj-Zj < 0R13= R03 - 2 R12

03-2 R1


Cj-Zj < 0

11R1213Cj-Zj < 0R13= R03 - 2 R12

03-2 R1


Cj-Zj < 0

11R1213Cj-Zj < 0R13= R03 - 2 R12

03-2 R1


Cj-Zj < 0

11R1213Cj-Zj < 0R13= R03 - 2 R12

03-2 R1


Cj-Zj < 0

11R1213Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213

10/(2/3)=15

No2/(8/3) = 3/4

Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213

10/(2/3)=15

No2/(8/3) =

Cj-Zj < 0

01R0203ITERACION 1

Cj-Zj < 0

11R1213

Cj-Zj < 0

Fila pivote

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0R21= R1

-2/3 R23

11-2/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R21= R1

-2/3 R23

11-2/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R21= R1

-2/3 R23

11-2/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R21= R1

-2/3 R23

11-2/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R22= R12 +1/3 R23

12+1/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R22= R12 +1/3 R23

12+1/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R22= R12 +1/3 R23

12+1/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0R22= R12 +1/3 R23

12+1/3 R2


Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223

(19/2)/(1/4) NoNo

Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223

38 NoNo

Cj-Zj < 0

11R1213ITERACION 2

Cj-Zj < 0

21R2223

Fila

pivote

Cj-Zj < 0

212223ITERACION 2

Cj-Zj < 0

21R2223

Fila

pivote

Cj-Zj < 0

212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0

212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0

212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0

212223ITERACION 3

Cj-Zj < 0

313233

R31 = R21 x 4

Cj-Zj < 0

212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R32= R22 +1/8 R31

22+1/8 R3

32212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R32= R22 +1/8 R31

22+1/8 R3

32212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R32= R22 +1/8 R31

22+1/8 R3

R3212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R32= R22 +1/8 R31

22+1/8 R3

R3212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R33= R23 +3/8 R31

23+3/8 R3

33212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R33= R23 +3/8 R31

23+3/8 R3

33212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R33= R23 +3/8 R31

23+3/8 R3

R3212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0R33= R23 +3/8 R31

23+3/8 R3

R3212223ITERACION 3

Cj-Zj < 0

313233Cj-Zj < 0

212223ITERACION 3

Cj-Zj < 0

313233

Ya que todos los Cj Zj < 0 entonces la tabla es ptima. Lasolucin es: X1 = 6, X2 = 15 y s2 = 38, y el valor de Z = 72.

Cj-Zj < 0

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B-1

6

21

-2

22

2

11

0

00

0

-10

1

00

0

19

6

4Zj

Cj - Zj

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

6

2

1

-2

2

2

2

1

1

0

0

0

0

-1

0

1

0

0

0

1

9

6

4Zj

Cj - Zj

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

6

2

1

-2

2

2

2

1

1

0

0

0

0

-1

0

1

0

0

0

1

9

6

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

6

2

1

-2

2

2

2

1

1

0

0

0

0

-1

0

1

0

0

0

1

9

6

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

2+8M

4

3+3M

0

-M

0

0

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

6

2

1

-2

2

2

2

1

1

0

0

0

0

-1

0

1

0

0

0

1

9

6

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

2+8M

4

3+3M

0

-M

0

0

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

6

2

1

-2

2

2

2

1

1

0

0

0

0

-1

0

1

0

0

0

1

9

6

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

2+8M

4

3+3M

0

-M

0

0

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

6

2

1

-2

2

2

2

1

1

0

0

0

0

-1

0

1

0

0

0

1

9

6

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

2+8M

4

3+3M

0

-M

0

0

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

1

2

1

0

0

0

9

6

-2

2

0

0

1

0

6

2

2

1

0

-1

0

1

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

2+8M

4

3+3M

0

-M

0

0

Cj

2

4

3

0

0

-M

-M

CB

VB

X1

X2

X3s1s2a1a2

B

0

-M

-Ms1 a1 a2

-1

1

2

1

0

0

0

9

6

-2

2

0

0

1

0

6

2

2

1

0

-1

0

1

4Zj-8M0-3M0M-M-M

-10M

Cj - Zj

2+8M

4

3+3M

0

-M

0

0

R

R

Cj24300-M-MCBVBX1X2X3s1s2a1a2B0

-M

-Ms1 a1

a2-112100096-22001062210-1014Zj-8M0-3M0M-M-M-10MCj - Zj2+8M43+3M0-M00

R

R


2

-Ms1

X1 a201

0

00

0

110ZjCj - Zj

R

R


-M

-Ms1 a1


R

R


2

-Ms1

X1 a20

1

01

0

00

0

1ZjCj - Zj

R

R


-M

-Ms1 a1


R

R


2

-Ms1

X1 a20

1

0

-1/3

1/31

0

0

0

1/60

0

1

1ZjCj - Zj

R

R

R

R


2

-Ms1

X1 a20

1

0

-1/3

1/31

0

0

0

1/60

0

1

1ZjCj - Zj

R

2

R


-M

-Ms1 a1


R

-11210009

R

R

R

R


2

-Ms1

X1 a20

1

0

-1/3

1/31

0

0

0

1/60

0

1

1ZjCj - Zj

R

2

R


-M

-Ms1 a1


R

-1

11

-1/32

1/31

00

00

1/60

09

1

R

R

R

R


2

-Ms1

X1 a20

1

0

-1/3

1/31

0

0

0

1/60

0

1

1ZjCj - Zj

R

-1

11

-1/32

1/31

00

00

1/60

09

102/37/3101/6010

2

R


-M

-Ms1 a1


1

R

R

R

R


2

-Ms1

X1 a20

1

02/3

-1/37/3

1/31

0

00

01/6

1/60

0

110

1ZjCj - Zj

R

-1

11

-1/32

1/31

00

00

1/60

09

102/37/3101/6010

2

R


-M

-Ms1 a1


1

R

R

R

R


2

-Ms1

X1 a20

1

02/3

-1/37/3

1/31

0

00

01/6

1/60

0

110

1ZjCj - Zj

R

2


-M

-Ms1 a1


R

2210-1014

R

R

R

R


2

-Ms1

X1 a20

1

02/3

-1/37/3

1/31

0

00

01/6

1/60

0

110

1ZjCj - Zj

R

2


-M

-Ms1 a1


R

2

-22

2/31

-2/30

0-1

00

-1/31

04

-2

R

R

R

R


2

-Ms1

X1 a20

1

02/3

-1/37/3

1/31

0

00

01/6

1/60

0

110

1ZjCj - Zj

2

-22

2/31

-2/30

0-1

00

-1/31

04

-208/31/30-1-1/312

R

2


-M

-Ms1 a1


3

R

R

R

R


2

-Ms1

X1 a20

1

02/3

-1/3

8/37/3

1/3

1/31

0

00

0

-11/6

1/6

-1/30

0

110

1

2ZjCj - Zj

2

-22

2/31

-2/30

0-1

00

-1/31

04

-208/31/30-1-1/312

R

2


-M

-Ms1 a1


3

R

R


-M

-Ms1 a1


R

R


2

-Ms1

X1 a20

1

02/3

-1/3

8/37/3

1/3

1/31

0

00

0

-11/6

1/6

-1/30

0

110

1

2Zj2

-2/3-8M/3

2/3-M/30M

1/3+M/3-M2-2MCj - Zj

R

R


-M

-Ms1 a1


R

R


2

-Ms1

X1 a20

1

02/3

-1/3

8/37/3

1/3

1/31

0

00

0

-11/6

1/6

-1/30

0

110

1

2Zj2

-2/3-8M/3

2/3-M/30M

1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


-M

-Ms1 a1


R

R


2

-Ms1

X1 a20

1

02/3

-1/3

8/37/3

1/3

1/31

0

00

0

-11/6

1/6

-1/30

0

110

1

2Zj2

-2/3-8M/3

2/3-M/30M

1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R

R

R


-M

-Ms1 a1



2

-Ms1

X1 a20

1

02/3

-1/3

8/37/3

1/3

1/31

0

00

0

-11/6

1/6

-1/30

0

110

1

2Zj2

-2/3-8M/3

2/3-M/30M

1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R

R

R


-M

-Ms1 a1



2

-Ms1

X1 a20

1

02/3

-1/3

8/37/3

1/3

1/31

0

00

0

-11/6

1/6

-1/30

0

110

1

2Zj2

-2/3-8M/3

2/3-M/30M

1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


-M

-Ms1 a1


R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R

Cj24300-M-MCBVBX1X2X3s1s2a1a2BZjCj - Zj

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X2ZjCj - Zj

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X20

1

00

01

0

01ZjCj - Zj

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X20

1

00

0

11

0

0ZjCj - Zj

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X20

1

00

0

1

1/81

0

0

-3/8

-1/8

3/8

3/4ZjCj - Zj

R

R

R

R


2

4s1

X1

X20

1

00

0

1

1/81

0

0

-3/8

-1/8

3/8

3/4ZjCj - Zj

1

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

02/37/3101/6010

R

R

R

R


2

4s1

X1

X20

1

00

0

1

1/81

0

0

-3/8

-1/8

3/8

3/4ZjCj - Zj

1

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

0

02/3

-2/37/3

-1/121

00

1/41/6

1/120

-1/410

-1/2

R

R

R

R


2

4s1

X1

X20

1

00

0

1

1/81

0

0

-3/8

-1/8

3/8

3/4ZjCj - Zj

1

0

02/3

-2/37/3

-1/121

00

1/41/6

1/120

-1/410

-1/2009/411/41/4-1/419/2

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

1

R

R

R

R


2

4s1

X1

X20

1

00

0

19/4

1/81

0

01/4

-3/81/4

-1/8-1/4

3/819/2

3/4ZjCj - Zj

1

0

02/3

-2/37/3

-1/121

00

1/41/6

1/120

-1/410

-1/2009/411/41/4-1/419/2

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

1

R

R

R

R


2

4s1

X1

X20

1

00

0

19/4

1/81

0

01/4

-3/81/4

-1/8-1/4

3/819/2

3/4ZjCj - Zj

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

1-1/31/3001/601

R

R

R

R


2

4s1

X1

X20

1

00

0

19/4

1/81

0

01/4

-3/81/4

-1/8-1/4

3/819/2

3/4ZjCj - Zj

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

1

0-1/3

1/31/3

1/240

00

-1/81/6

-1/240

1/81

1/4

R

R

R

R


2

4s1

X1

X20

1

00

0

19/4

1/81

0

01/4

-3/81/4

-1/8-1/4

3/819/2

3/4ZjCj - Zj

1

0-1/3

1/31/3

1/240

00

-1/81/6

-1/240

1/81

1/4103/80-1/81/81/85/4

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

2

R

R

R

R


2

4s1

X1

X20

1

00

0

19/4

3/8

1/81

0

01/4

-1/8

-3/81/4

1/8

-1/8-1/4

1/8

3/819/2

5/4

3/4ZjCj - Zj

1

0-1/3

1/31/3

1/240

00

-1/81/6

-1/240

1/81

1/4103/80-1/81/81/85/4

R

3


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

2

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X20

1

00

0

19/4

3/8

1/81

0

01/4

-1/8

-3/81/4

1/8

-1/8-1/4

1/8

3/819/2

5/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X20

1

00

0

19/4

3/8

1/81

0

01/4

-1/8

-3/81/4

1/8

-1/8-1/4

1/8

3/819/2

5/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0

R

R


2

4s1

X1

X20

1

00

0

19/4

3/8

1/81

0

01/4

-1/8

-3/81/4

1/8

-1/8-1/4

1/8

3/819/2

5/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0


2

4s1

X1

X20

1

00

0

19/4

3/8

1/81

0

01/4

-1/8

-3/81/4

1/8

-1/8-1/4

1/8

3/819/2

5/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0


2

4s1

X1

X20

1

00

0

19/4

3/8

1/81

0

01/4

-1/8

-3/81/4

1/8

-1/8-1/4

1/8

3/819/2

5/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R

R


2

-Ms1

X1 a20

12/3

-1/37/3

1/31

00

01/6

1/60

010

108/31/30-1-1/312Zj2-2/3-8M/32/3-M/30M1/3+M/3-M2-2M

Cj - Zj

0(14+8M)

3

7/3+M/3

0

-M

-1/3-4M/3

0


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R

R

R


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R

Cj24300-M-MCBVBX1X2X3s1s2a1a2BZjCj - Zj

R

R

R


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R


2

4s2

X1

X2ZjCj - Zj

R

R

R


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R


2

4s2

X1

X20

1

00

0

110

0ZjCj - Zj

R

R

R

R

R

R


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4


2

4s2

X1

X20

1

00

0

1941

0

01-138ZjCj - Zj

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

1941

0

01-138ZjCj - Zj

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

103/80-1/81/81/85/4

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

1941

0

01-138ZjCj - Zj

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

1

00

03/8

9/80

1/2-1/8

1/81/8

1/81/8

-1/85/4

19/4

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

1941

0

01-138ZjCj - Zj

1

00

03/8

9/80

1/2-1/8

1/81/8

1/81/8

-1/85/4

19/4103/21/201/406

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

2

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

19

3/24

1/21

0

01

1/4-1

038

6ZjCj - Zj

1

00

03/8

9/80

1/2-1/8

1/81/8

1/81/8

-1/85/4

19/4103/21/201/406

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

2

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

19

3/24

1/21

0

01

1/4-1

038

6ZjCj - Zj

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

011/80-3/8-1/83/83/4

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

19

3/24

1/21

0

01

1/4-1

038

6ZjCj - Zj

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

0

01

01/8

27/80

3/2-3/8

3/8-1/8

3/83/8

-3/83/4

57/4

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

19

3/24

1/21

0

01

1/4-1

038

6ZjCj - Zj

0

01

01/8

27/80

3/2-3/8

3/8-1/8

3/83/8

-3/83/4

57/4017/23/201/4015

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

3

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

19

3/2

7/24

1/2

3/21

0

01

1/4

1/4-1

0

038

6

15ZjCj - Zj

0

01

01/8

27/80

3/2-3/8

3/8-1/8

3/83/8

-3/83/4

57/4017/23/201/4015

R

1


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

3

R

R

R


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

R

R

R


2

4s2

X1

X20

1

00

0

19

3/2

7/24

1/2

3/21

0

01

1/4

1/4-1

0

038

6

15Zj2417703/2072Cj - Zj

R

R

R

R

R

R


2

4s2

X1

X20

1

00

0

19

3/2

7/24

1/2

3/21

0

01

1/4

1/4-1

0

038

6

15Zj2417703/2072Cj - Zj00-14-70-3/2-M-M


2

4s1

X1

X2009/411/41/4-1/419/21

00

13/8

1/80

0-1/8

-3/81/8

-1/81/8

3/85/4

3/4Zj245/40-7/4-1/47/411/2Cj - Zj007/407/4-M+1/4-M-7/4

Documents

9 Metodo Simplex Mayor Maximizacion