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metodo-dual
1.
RUBÍ PARRA QUINTO
SEMESTRE “A” Página 1 MÉTODO DUAL SE LO OBTIENE A TRAVES DEL MÉTODO PRIMAL MAXIMIZAR Z= 400 A + 300 B SA 2 A + B ≤ 60 A + 3 B ≤ 40 A + B ≤ 30 A,B ≥ 0 VB VARIABLES VALOR Z A B H1 H2 H3 Z 1 -400 -300 0 0 0 0 H1 0 2 1 1 0 0 60 H2 0 1 3 0 1 0 40 H3 0 1 1 0 0 1 30 Z 1 0 100 0 0 400 12000 H1 0 0 -1 1 0 -2 0 H2 0 0 2 0 1 -1 10 A 0 1 1 0 0 -1 30 SO Z= 12000 VO A=30 B=0 H1=0 H2=10 H3=0
2.
RUBÍ PARRA QUINTO
SEMESTRE “A” Página 2 MÉTODO DUAL MINIMIZAR Z= 60 Y1 + 40 Y2 + 30 Y3 SA 2 Y1 +Y2 +Y3 ≥ 400 Y1 + 3Y2 + Y3 ≥300 Yi≥0 2Y1 + Y3 = 400 100 + Y3 = 300 -Y1 – Y3 = -300 Y3= 200 Y1 = 100 SO Z= 12000 COMP. Z= 60(100) + 40(0) + 30(200) VO Y1= 100 Z= 12000 Y2= 0 Y3= 200 MÉTODO PRIMAL MINIMIZAR Z= 4X1 + 7X2 SA X1 ≤6 2X2= 14 3X1 + 2X2 ≥ 20
3.
RUBÍ PARRA QUINTO
SEMESTRE “A” Página 3 FORMA CANÓNICA Z= 4X1 + 7X2 + OH1 + OH2 + MA1 + MA2 X1 + H1 =6 2X2 + A1 =14 (-M) 3X1 + 2X2 -H2 +A2 =20 (-M) -Z + 4X1 + 7X2 + OH1 + OH2 + MA1 + MA2 =0 -2MX2 -MA1 =-14M -3MX1 -2MX2 MH2 -MA2 =-20M VB VARIABLES VALOR Z X1 X2 H1 H2 A1 A2 Z -1 (-)3M+4 (-)4M+7 0 M 0 0 (-)34M H1 0 1 0 1 0 0 0 4 A1 0 0 2 0 0 1 0 12 A2 0 3 2 0 -1 0 1 18 Z -1 (-)3M+4 0 0 M 2M-7/2 0 (-)6M-49 H1 0 1 0 1 0 0 0 4 X2 0 0 1 0 0 1/2 0 6 A2 0 3 0 0 -1 -1 1 6 Z -1 0 0 0 4/3 M-13/6 M-4/3 -57 H1 0 0 0 1 1/3 1/3 - 1/3 4 X2 0 0 1 0 0 1/2 0 7 X1 0 1 0 0 - 1/3 - 1/3 1/3 2 SO -Z= -57 Z=57 VO X1=2 H1=4 X2=7 H2=0
4.
RUBÍ PARRA QUINTO
SEMESTRE “A” Página 4 MÉTODO DUAL MAXIMIZAR Z= 6Y1 + 14Y2 + 20Y3 SA Y1 + 3Y3 ≥4 (2) 2Y2 + 2Y3 <> 7 (-3) Yi≥0 + 6Y3 = 8 2(13/6)+2Y3=7 -6Y2 -6Y3 = -21 13/3 + 2Y3=7 Y2 = 13/6 Y3=4/3 SO Z= 57 COMP. Z= 6(0) + 14(13/6) + 20(4/3) VO Y1= 0 Z= 0 + 91/3 + 80/3 Y2= 13/6 Z= 57 Y3= 4/3 METODO PRIMAL MAXIMIZAR Z= 4X1 + 7X2 SA X1 ≤ 4 2X2 ≤ 12 3X1 + 2X2 = 18 Xi ≥ 0
5.
RUBÍ PARRA QUINTO
SEMESTRE “A” Página 5 SO Z= 50 VO X1=2 H1=2 X2=6 H2=0 MÉTODO DUAL MINIMIZAR Z= 4Y1 + 12Y2 + 18Y3 SA Y1 + 3Y3≥ 4 2Y2 + 2Y3≥ 7 Yi≥ 0 3Y3= 4 2Y2 + 2(4/3) = 7 Y3=4/3 Y2= 13/6 SO Z=50 COMP. Z= 4(0) + 12(13/6) + 18(4/3) VO Y1=0 Z= 0 + 26 +24 Y2= 13/6 Z= 50 Y3= 4/3
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