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