ejercicios resueltos.minimizacion.docx
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X1 X2 SIMBOLO LD
FO 3 4 MINIMIZAR
R1 4 9 > 60
R2 5 -3 < 70
R3 6 -2 = 50
X1 X2 H3 A4 H5 A6 LD
FO 3 -10M 4 -7M 0+1M 0+0M 0+0M 0+0M 0 -110M
A4 4 9 -1 1 0 0 60
H5 5 -3 0 0 1 0 70
A6 6 -2 0 0 0 1 50
X1 X2 H3 A4 H5 A6 LD
FO 0+0M 5 -31/3M 0+1M 0+0M 0+0M -1/2+5/3M -25 -80/3M
A4 0 31/3 -1 1 0 -2/3 80/3
H5 0 -4/3 0 0 1 -5/6 85/3
X1 1 -1/3 0 0 0 1/6 25/3
X1 X2 H3 A4 H5 A6 LD
FO 0+0M 0+0M 15/31+0M -15/31+1M 0+0M -11/62+1M -1175/31+0M
X2 0 1 -3/31 3/31 0 -2/31 80/31
H5 0 0 -4/31 4/31 1 -57/62 985/31
X1 1 0 -1/31 1/31 0 9/62 285/31
RESPUESTA:SOLUCION UNICA
X1 = 9,19
X2 = 2,58
H3 = 0
A4 = 0 Xi = VARIABLE ORIGINAL
H5 = 31,77 Hi = VARIABLE DE HOLGURA/SUPERAVIT
A6 = 0 Ai = VARIABLE ARTIFICIAL
Z = 37,9032258064516 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 SIMBOLO LD
FO 3 4 MINIMIZAR
R1 5 8 = 60
R2 5 6 < 60
R3 3 8 > 40
X1 X2 A3 H4 H5 A6 LD
FO 3 -8M 4 -16M 0+0M 0+0M 0+1M 0+0M 0 -100M
A3 5 8 1 0 0 0 60
H4 5 6 0 1 0 0 60
A6 3 8 0 0 -1 1 40
X1 X2 A3 H4 H5 A6 LD
FO 3/2 -2M 0+0M 0+0M 0+0M 1/2 -1M -1/2+2M -20 -20M
A3 2 0 1 0 1 -1 20
H4 11/4 0 0 1 3/4 -3/4 30
X2 3/8 1 0 0 -1/8 1/8 5
X1 X2 A3 H4 H5 A6 LD
FO 0+0M 0+0M -3/4+1M 0+0M -1/4+0M 1/4+1M -35+0M
X1 1 0 1/2 0 1/2 -1/2 10
H4 0 0 -11/8 1 -5/8 5/8 5/2
X2 0 1 -3/16 0 -5/16 5/16 5/4
X1 X2 A3 H4 H5 A6 LD
FO 1/2+0M 0+0M -1/2+1M 0+0M 0+0M 0+1M -30+0M
H5 2 0 1 0 1 -1 20
H4 5/4 0 -3/4 1 0 0 15
X2 5/8 1 1/8 0 0 0 15/2
RESPUESTA:
X1 = 0
X2 = 7,5
A3 = 0
H4 = 15 Xi = VARIABLE ORIGINAL
H5 = 20 Hi = VARIABLE DE HOLGURA/SUPERAVIT
A6 = 0 Ai = VARIABLE ARTIFICIAL
Z = 30 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 SIMBOLO LD
FO 4 7 MINIMIZAR
R1 6 6 = 50
R2 8 5 = 60
R3 2 6 > 40
R4 4 6 < 60
X1 X2 A3 A4 H5 A6 H7 LD
FO 4 -16M 7 -17M 0+0M 0+0M 0+1M 0+0M 0+0M 0 -150M
A3 6 6 1 0 0 0 0 50
A4 8 5 0 1 0 0 0 60
A6 2 6 0 0 -1 1 0 40
H7 4 6 0 0 0 0 1 60
X1 X2 A3 A4 H5 A6 H7 LD
FO 5/3 -31/3M 0+0M 0+0M 0+0M 7/6 -11/6M -7/6+17/6M 0+0M-140/3 -110/3M
A3 4 0 1 0 1 -1 0 10
A4 19/3 0 0 1 5/6 -5/6 0 80/3
X2 1/3 1 0 0 -1/6 1/6 0 20/3
H7 2 0 0 0 1 -1 1 20
X1 X2 A3 A4 H5 A6 H7 LD
FO 0+0M 0+0M-
5/12+31/12M
0+0M 3/4+3/4M -3/4+1/4M 0+0M-305/6 -65/6M
X1 1 0 1/4 0 1/4 -1/4 0 5/2
A4 0 0 -19/12 1 -3/4 3/4 0 65/6
X2 0 1 -1/12 0 -1/4 1/4 0 35/6
H7 0 0 -1/2 0 1/2 -1/2 1 15
RESPUESTA: SIN SOLUCION FACTIBLE, Ai<>0 EN LA RESPUESTA !
X1 = 2,5
X2 = 5,83
A3 = 0
A4 = 10,83
H5 = 0 Xi = VARIABLE ORIGINAL
A6 = 0 Hi = VARIABLE DE HOLGURA/SUPERAVIT
H7 = 15 Ai = VARIABLE ARTIFICIAL
Z = 50,8333333333333 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 SIMBOLO LD
FO 6 5 MINIMIZAR
R1 5 6 > 40
R2 6 7 = 50
R3 3 9 < 60
X1 X2 H3 A4 A5 H6 LD
FO 6 -11M 5 -13M 0+1M 0+0M 0+0M 0+0M 0 -90M
A4 5 6 -1 1 0 0 40
A5 6 7 0 0 1 0 50
H6 3 9 0 0 0 1 60
X1 X2 H3 A4 A5 H6 LD
FO 11/6 -1/6M 0+0M 5/6 -7/6M -5/6+13/6M 0+0M 0+0M-100/3 -10/3M
X2 5/6 1 -1/6 1/6 0 0 20/3
A5 1/6 0 7/6 -7/6 1 0 10/3
H6 -9/2 0 3/2 -3/2 0 1 0
X1 X2 H3 A4 A5 H6 LD
FO 12/7+0M 0+0M 0+0M 0+1M -5/7+1M 0+0M -250/7+0M
X2 6/7 1 0 0 1/7 0 50/7
H3 1/7 0 1 -1 6/7 0 20/7
H6 -33/7 0 0 0 -9/7 1 -30/7
RESPUESTA:
X1 = 0
X2 = 7,14
H3 = 2,86
A4 = 0 Xi = VARIABLE ORIGINAL
A5 = 0 Hi = VARIABLE DE HOLGURA/SUPERAVIT
H6 = -4,28571428571428
Ai = VARIABLE ARTIFICIAL
Z = 35,7142857142857 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 SIMBOLO LD
FO 3 8 MINIMIZAR
R1 5 3 = 50
R2 -3 5 > 30
R3 -4 6 < 50
R4 3 7 = 45
R5 3 5 > 60
X1 X2 A3 H4 A5 H6 A7 H8 A9 LD
FO 3 -8M 8 -20M 0+0M 0+1M 0+0M 0+0M 0+0M 0+1M 0+0M 0 -185M
A3 5 3 1 0 0 0 0 0 0 50
A5 -3 5 0 -1 1 0 0 0 0 30
H6 -4 6 0 0 0 1 0 0 0 50
A7 3 7 0 0 0 0 1 0 0 45
A9 3 5 0 0 0 0 0 -1 1 60
X1 X2 A3 H4 A5 H6 A7 H8 A9 LD
FO 39/5 -20M 0+0M 0+0M 8/5 -3M -8/5+4M 0+0M 0+0M 0+1M 0+0M -48 -65M
A3 34/5 0 1 3/5 -3/5 0 0 0 0 32
X2 -3/5 1 0 -1/5 1/5 0 0 0 0 6
H6 -2/5 0 0 6/5 -6/5 1 0 0 0 14
A7 36/5 0 0 7/5 -7/5 0 1 0 0 3
A9 6 0 0 1 -1 0 0 -1 1 30
X1 X2 A3 H4 A5 H6 A7 H8 A9 LD
FO 0+0M 0+0M 0+0M 1/12+8/9M -1/12+1/9M 0+0M-
13/12+25/9M
0+1M 0+0M-205/4 -170/3M
A3 0 0 1 -13/18 13/18 0 -17/18 0 0 175/6
X2 0 1 0 -1/12 1/12 0 1/12 0 0 25/4
H6 0 0 0 23/18 -23/18 1 1/18 0 0 85/6
X1 1 0 0 7/36 -7/36 0 5/36 0 0 5/12
A9 0 0 0 -1/6 1/6 0 -5/6 -1 1 55/2
RESPUESTA: SIN SOLUCION FACTIBLE, Ai<>0 EN LA RESPUESTA !
X1 = 0,42
X2 = 6,25
A3 = 29,17
H4 = 0
A5 = 0
H6 = 14,17
A7 = 0 Xi = VARIABLE ORIGINAL
H8 = 0 Hi = VARIABLE DE HOLGURA/SUPERAVIT
A9 = 27,5 Ai = VARIABLE ARTIFICIAL
Z = 51,25 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 SIMBOLO LD
FO 4 9 MINIMIZAR
R1 7 6 = 50
R2 8 5 > 40
R3 5 8 < 90
R4 4 2 > 60
X1 X2 A3 H4 A5 H6 H7 A8 LD
FO 4 -19M 9 -13M 0+0M 0+1M 0+0M 0+0M 0+1M 0+0M 0 -150M
A3 7 6 1 0 0 0 0 0 50
A5 8 5 0 -1 1 0 0 0 40
H6 5 8 0 0 0 1 0 0 90
A8 4 2 0 0 0 0 -1 1 60
X1 X2 A3 H4 A5 H6 H7 A8 LD
FO 0+0M 13/2 -9/8M 0+0M 1/2 -11/8M -1/2+19/8M 0+0M 0+1M 0+0M -20 -55M
A3 0 13/8 1 7/8 -7/8 0 0 0 15
X1 1 5/8 0 -1/8 1/8 0 0 0 5
H6 0 39/8 0 5/8 -5/8 1 0 0 65
A8 0 -1/2 0 1/2 -1/2 0 -1 1 40
X1 X2 A3 H4 A5 H6 H7 A8 LD
FO 0+0M39/7+10/7
M-4/7+11/7M 0+0M 0+1M 0+0M 0+1M 0+0M -200/7 -220/7M
H4 0 13/7 8/7 1 -1 0 0 0 120/7
X1 1 6/7 1/7 0 0 0 0 0 50/7
H6 0 26/7 -5/7 0 0 1 0 0 380/7
A8 0 -10/7 -4/7 0 0 0 -1 1 220/7
RESPUESTA: SIN SOLUCION FACTIBLE, Ai<>0 EN LA RESPUESTA !
X1 = 7,14
X2 = 0
A3 = 0
H4 = 17,14
A5 = 0
H6 = 54,29 Xi = VARIABLE ORIGINAL
H7 = 0 Hi = VARIABLE DE HOLGURA/SUPERAVIT
A8 = 31,43 Ai = VARIABLE ARTIFICIAL
Z = 28,5714285714286 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 X3 SIMBOLO LD
FO 2 3 4 MINIMIZAR
R1 3 2 0 = 50
R2 2 -2 3 > 0
R3 3 4 5 < 80
X1 X2 X3 A4 H5 A6 H7 LD
FO 2 -5M 3+0M 4 -3M 0+0M 0+1M 0+0M 0+0M 0 -50M
A4 3 2 0 1 0 0 0 50
A6 2 -2 3 0 -1 1 0 0
H7 3 4 5 0 0 0 1 80
X1 X2 X3 A4 H5 A6 H7 LD
FO 0+0M 5 -5M 1+9/2M 0+0M 1 -3/2M -1+5/2M 0+0M 0 -50M
A4 0 5 -9/2 1 3/2 -3/2 0 50
X1 1 -1 3/2 0 -1/2 1/2 0 0
H7 0 7 1/2 0 3/2 -3/2 1 80
X1 X2 X3 A4 H5 A6 H7 LD
FO 0+0M 0+0M 11/2+0M -1+1M -1/2+0M 1/2+1M 0+0M -50+0M
X2 0 1 -9/10 1/5 3/10 -3/10 0 10
X1 1 0 3/5 1/5 -1/5 1/5 0 10
H7 0 0 34/5 -7/5 -3/5 3/5 1 10
X1 X2 X3 A4 H5 A6 H7 LD
FO 0+0M 5/3+0M 4+0M -2/3+1M 0+0M 0+1M 0+0M -100/3+0M
H5 0 10/3 -3 2/3 1 -1 0 100/3
X1 1 2/3 0 1/3 0 0 0 50/3
H7 0 2 5 -1 0 0 1 30
RESPUESTA: SOLUCION UNICA
X1 = 16,67
X2 = 0
X3 = 0
A4 = 0
H5 = 33,33 Xi = VARIABLE ORIGINAL
A6 = 0 Hi = VARIABLE DE HOLGURA/SUPERAVIT
H7 = 30 Ai = VARIABLE ARTIFICIAL
Z = 33,3333333333333 Z = VALOR DE LA FUNCION OBJETIVO (FO)
X1 X2 SIMBOLO LD
FO 3 5 MINIMIZAR
R1 -2 3 < 0
R2 4 2 > 0
R3 3 5 = 5
R4 2 2 < 20
R5 3 5 < 40
X1 X2 H3 H4 A5 A6 H7 H8 LD
FO 3 -7M 5 -7M 0+0M 0+1M 0+0M 0+0M 0+0M 0+0M 0 -5M
H3 -2 3 1 0 0 0 0 0 0
A5 4 2 0 -1 1 0 0 0 0
A6 3 5 0 0 0 1 0 0 5
H7 2 2 0 0 0 0 1 0 20
H8 3 5 0 0 0 0 0 1 40
X1 X2 H3 H4 A5 A6 H7 H8 LD
FO 0+0M 7/2 -7/2M 0+0M 3/4 -3/4M -3/4+7/4M 0+0M 0+0M 0+0M 0 -5M
H3 0 4 1 -1/2 1/2 0 0 0 0
X1 1 1/2 0 -1/4 1/4 0 0 0 0
A6 0 7/2 0 3/4 -3/4 1 0 0 5
H7 0 1 0 1/2 -1/2 0 1 0 20
H8 0 7/2 0 3/4 -3/4 0 0 1 40
X1 X2 H3 H4 A5 A6 H7 H8 LD
FO 0+0M 0+0M -7/8+7/8M19/16 -19/16M
-19/16+35/16
M0+0M 0+0M 0+0M 0 -5M
X2 0 1 1/4 -1/8 1/8 0 0 0 0
X1 1 0 -1/8 -3/16 3/16 0 0 0 0
A6 0 0 -7/8 19/16 -19/16 1 0 0 5
H7 0 0 -1/4 5/8 -5/8 0 1 0 20
H8 0 0 -7/8 19/16 -19/16 0 0 1 40
X1 X2 H3 H4 A5 A6 H7 H8 LD
FO 0+0M 0+0M 0+0M 0+0M 0+1M -1+1M 0+0M 0+0M -5+0M
X2 0 1 3/19 0 0 2/19 0 0 10/19
X1 1 0 -5/19 0 0 3/19 0 0 15/19
H4 0 0 -14/19 1 -1 16/19 0 0 80/19
H7 0 0 4/19 0 0 -10/19 1 0 330/19
H8 0 0 0 0 0 -1 0 1 35
RESPUESTA: SOLUCION UNICA
X1 = 0,79
X2 = 0,53
H3 = 0
H4 = 4,21
A5 = 0
A6 = 0 Xi = VARIABLE ORIGINAL
H7 = 17,37 Hi = VARIABLE DE HOLGURA/SUPERAVIT
H8 = 35 Ai = VARIABLE ARTIFICIAL
Z = 5 Z = VALOR DE LA FUNCION OBJETIVO (FO)