Subido por Susana Hernández

Doble Fase Ejercicio 4 Tarea 25

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EJERCICIO 4
SALA 2
GALAN DIAZ MARIAM SOANY
HERNANDEZ MOLINA SUSANA MARIA
NERIA YEPEZ ALEXANDRO AUGUSTO
NOTA: profe, tenemos dudas en el
inicio de la fase 2, ya que
no sabemos si realizamos bien
la obtención de los valores
unitarios en la función objetivo
MIN Z=8X1+16X2
SUJETO A:
8X1+8X2>=16
4X1+8X3>=8
2X1+2X2=6
DONDE:
X1 Y X2 >=0
FASE 1
8X1+8X2-W1+A1=16
4X1+8X3-W2+A2=8
2X1+2X2+A3=6
FUNCION OBJETIVO:
MIN Z= A1+A2+A3
MIN Z=-A1-A2-A3
TABLA 1
BASE Z X1 X2 W1 W2 A1 A2 A3 SOL
Z
10 0 0
0
-1 -1 -1 0
Z
1 14 18 -1 -1 0 0 0 30
A1
0 8 8 -1 0
A2
04 8 0
-1 0 1 0 8
8/8=1 R3T2=R3T1/8
A3
02 2 0
0
6/2=3 R4T2=R3T2(-2)+R4T1
R1T2=R3T2(-18)+R1T1
1 0 0 16 16/8=2 R2T2=R3T2(-8)+R2T1
0 0 1 6
BASE X2 R3T2=R3T1/8
Z X1 X2 W1 W2 A1 A2 A3 SOL
0/8 4/8 8/8 0/8 -1/8 0/8 1/8 0/8 8/8
0
1/2 1
0
-1/8 0
1/8 0
BASE A1 R2T2=R3T2(-8)+R2T1
Z
X1 X2 W1 W2
A1
1
A2
A3
SOL
0(-8) ½(-8) 1(-8) 0(-8) -1/8(-8) 0(-8) 1/8(-8) 0(-8) 1(-8)
0
-4
-8
0
1
0
-1
0
-8
0
8
8
-1
0
1
0
0
16
0
4
0
-1
1
1
-1
0
A1
A2
BASE Z R1T2=R3T2(-18)+R1T1
Z
X1
X2
W1 W2
8
A3
SOL
0(.18) ½(-18) 1(-18) 0(-18) -1/8(-18) 0(-18) 1/8(-18) 0(-18) 1(-18)
0
-9
-18
0
9/4
0
-9/4
0
-18
1
14
18
-1
-1
0
0
0
30
1
5
0
-1
5/4
0
-9/4
0
12
BASE A3 R4T2=R3T2(-2)+R4T1
Z
X1
X2 W1 W2
A1
A2
A3
SOL
0(-2) 1/2(-2) 1(-2) 0(-2) -1/8(-2) 0(-2) 1/8(-2) 0(-2) 1(-2)
0
-1
-2
0
1/4
0
-1/4
0
-2
0
2
2
0
0
0
0
1
6
0
1
0
0
1/4
0
-1/4
1
4
TABLA 2
BASE Z X1 X2 W1 W2 A1 A2 A3 SOL
Z
15
0 -1 5/4 0 -9/4 0 12
A1
04
0 -1 1
X2
0 1/2 1 0
-1/8 0 1/8 0 1
1/(½)=2 R3T3=R2T3(-½)+R3T3
A3
01
1/4 0 -1/4 1 4
4/1=4
0 0
1 -1
0 8
R1T3=R2T3(-5)+R1T2
8/4=2
R2T3=R2T2/4
R4T3=R2T3(-1)+R4T2
BASE X1 R2T3=R2T2/4
Z X1 X2 W1 W2 A1 A2 A3 SOL
0/4 4/4 0/4 -1/4 1/4 1/4 -1/4 0/4 8/4
0
1
0
-1/4 1/4 1/4 -1/4 0
BASE Z R1T3=R2T3(-5)+R1T2
Z
X1 X2 W1 W2 A1
2
A2
A3
SOL
0(-5) 1(-5) 0(-5) -¼(-5) ¼(-5) ¼(-5) -¼(-5) 0(-5) 2(-5)
0
-5
0
5/4
-5/4 -5/4 5/4
1
5
0
-1
5/4 0
1
0
0
1/4
0
0
-9/4 0
-5/4 -1
BASE X2 R3T3=R2T3(-½)+R3T2
Z
X1 X2 W1 W2
A1
0
A2
-10
12
2
A3
SOL
0(-½) 1(-½) 0(-½) -¼(-½) 1/4(-½) ¼(-½) -¼(-½) 0(-½) 2(-½)
0
-1/2 0
1/8
-1/8
-1/8 1/8
0
-1
0
1/2 1
0
-1/8
0
1/8
0
1
0
0
1/8
-1/4
-1/8 1/4
0
0
1
BASE A3 R4T3=R2T3(-1)+R4T2
Z
X1 X2 W1 W2 A1
A2
A3
SOL
0(-1) 1(-1) 0(-1) -¼(-1) ¼(-1) ¼(-1) -¼(-1) 0(-1) 2(-1)
0
-1
0
1/4
-1/4 -1/4 1/4
0
1
0
0
1/4 0
0
0
0
1/4
0
0
-2
-1/4 1
-1/4 0
4
1
2
TABLA 3
BASE Z X1 X2 W1 W2 A1 A2 A3 SOL
Z
1 0 0 1/4 0
-5/4 -1
X1
0 1 0 -1/4 1/4 1/4 -1/4 0 2
2/(-¼)=-8 R2T4=R4T4(¼)+R2T3
X2
0 0 1 1/8 -1/4 -1/8 1/4 0 0
0/(1/8)=0 R3T4=R4T4(-1/8)+R3T3
A3
0 0 0 1/4 0
2/(¼)=8
-1/4 0
BASE W1 R4T4=R4T3/1/4
Z
X1 X2 W1 W2
0 2
R1T4=R4T4(-¼)+R1T3
1 2
A1
A2
A3
R4T4=R4T3/1/4
SOL
0/(¼) 0/(¼) 0/(¼) ¼/(¼) 0/(¼) -¼/(¼) 0/(¼) 1/(¼) 2/(¼)
0
0
0
1
0
-1
0
BASE X2 R3T4=R4T4(-1/8)+R3T3
Z
X1
X2
W1
W2
4
A1
8
A2
A3
SOL
0(-1/8) 0(-1/8) 0(-1/8) 1(-1/8) 0(-1/8) -1(-1/8) 0(-1/8) 4(-1/8) 8(-1/8)
0
0
0
-1/8
0
1/8
0
-1/2
-1
0
0
1
1/8
-1/4
-1/8
1/4
0
0
0
0
1
0
-1/4
0
1/4
-1/2
-1
BASE X1 R2T4=R4T4(¼)+R2T3
Z
X1 X2 W1 W2 A1 A2 A3 SOL
0(¼) 0(¼) 0(¼) 1(¼) 0(¼) -1(¼) 0(¼) 4(¼) 8(¼)
0
0
0
1/4 0
-1/4 0
0
1
0
-1/4 1/4 1/4 -1/4 0
2
0
1
0
0
4
1/4 0
-1
-1/4 -1
2
BASE Z R1T4=R4T4(-¼)+R1T3
Z
X1 X2 W1 W2 A1
A2
A3
SOL
0(-¼) 0(-¼) 0(-¼) 1(-¼) 0(-¼) -1(-¼) 0(-¼) 4(-¼) 8(-¼)
0
0
0
-1/4 0
1/4
1
0
0
1/4 0
1
0
0
0
0
0
-1
-2
-5/4 -1
0
2
-1
-1
0
-1
TABLA 4:
BASE Z X1 X2 W1 W2 A1 A2 A3 SOL SOLUCION
Z
10 0 0
0
-1
0
Z=0
X1
01 0 0
1/4 0 -1/4 -1
4
X1=4
X2
00 1 0
-1/4 0 1/4 -1/2 -1
X2=-1
0
W1=8
W1 0 0 0 1
-1 -1
-1 0
4
8
FUNCION OBJETIVO:
MIN Z=-A1-A2-A3=0
RESTRICCIONES:
8X1+8X2-W1+A1=16 8(4)+8(-1)-1(8)+0=16
4X1+8X3-W2+A2=8 4(4)+8(-1)-0-0=8
2X1+2X2+A3=6
2(4)+2(-1)+0=6
FASE 2:
FUNCION OBJETIVO:
MIN Z=8X1+16X2
MIN Z= -8X1-16X2
-8(4)-16(-1)=-16
BASE
Z X1
X2
W1
W2
SOL
Z
1
-8
-16
0
0
0
Z
1
0
0
0
2
-16
X1
0
1
0
0
1/4
4
*-8
X2
0
0
1
0
-1/4
-1
*-16
W1
0
0
0
1
0
8
*0
0
-8
0
0
-2
-32
0
0
-16
0
4
16
0
0
0
0
0
0
1
-8
-16
0
0
0
1
0
0
0
2
16
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