Mostrando entradas con la etiqueta metodos de optimizacion. Mostrar todas las entradas
Mostrando entradas con la etiqueta metodos de optimizacion. Mostrar todas las entradas

miércoles, 27 de julio de 2011

EL METODO ALGORITMO DE SIMPLES PARTE 5


13.Max  Z  =  60X1 + 40X2 + 35X3
            S.a.
                        2X1 +   X2 +   5X3  ≤  200
                        6X1 + 5X2 +   3X3  ≤  84
                        5X1 + 5X2 +   4X3  ≤  100
                                 X1 , X2 , X3    ≥  0
Forma Estandarizada :
         Max  Z  =  60X1 + 40X2 + 35X3 + 0S1 + 0S2 + 0S3
            S.a.
                        2X1 +   X2 +   5X3 + S1                    =  200
                        6X2 + 5X2 +   3X3         + S2            =  84
                        5X3 + 5X2 +   4X3                  + S3   =  100
                                            X1, X2, X3, S1, S2, S3   ≥  0


CJ
60
40
35
0
0
0

CB
XB
Bi
X1
X2
X3
S1
S2
S3
θK
0
S1
200
2
1
5
1
0
0
100
0
S2
84
6
5
3
0
1
0
14
0
S3
100
5
5
4
0
0
1
20

ZJ
0
0
0
0
0
0
0


ZJ         +
CJ
-60
-40
-35
0
0
0

0
S1
172
0
-2/3
4
1
-1/3
0
43
60
X1
14
1
5/6
1/2
0
1/6
0
28
0
S3
30
0
5/6
3/2
0
-5/6
1
20

ZJ
840
60
50
30
0
10
0


ZJ         +
CJ
0
10
-5
0
10
0

0
S1
92
0
-26/9
0
1
17/9
-8/3

60
X1
4
1
5/9
0
0
4/9
-1/3

35
X3
20
0
5/9
1
0
-5/9
2/3


ZJ
940
60
475/9
35
0
65/9
10/3


ZJ         +
CJ
0
115/9
0
0
65/9
10/3

EL METODO ALGORITMO DE SIMPLES PARTE 4


10.-      Max Z  =  2X1 +  4X2 + X3
S.a.
              X1 + 2X2 –   X3  ≤  5
                        2X1 –   X2 + 2X3  =  2
                        -X1 + 2X2 + 2X3  ≥  1
                           X1 , X2 , X3       ≥  0
Forma Estandarizada :
            Max Z  =  2X1 + 4X2 + X3 + 0S1 + 0S3 – MA2 – MA3
S.a.

                          X1 + 2X2 –   X3 + S1                          =  5
                        2X1 –   X2 + 2X3        + A2                  =  2
                        -X1 + 2X2 + 2X3                - S3 + A3    =  1
    



CJ
2
4
1
0
0
-M
-M

CB
XB
bI
X1
X2
X3
S3
S1
A1
A2
θ  K
0
S1
5
1
2
-1
0
1
0
0
-
-M
A1
2
2
-1
2
0
0
1
0
1
-M
A2
1
-1
2
2
-1
0
0
1
1/2

ZJ
-3M
-M
-M
-4M
M
0
-M
-M


ZJ     +
CJ
-M - 2
-M - 4
-4M - 1
-M
0
0
0

0
S1
11/2
1/2
3
0
-1/2
1
0
1/2
11
-M
A1
1
3
-3
0
1
0
1
-1
1/3
1
X3
1/2
-1/2
1
1
-1/2
0
0
1/2
-

ZJ
-M +1/2
-3M-1/2
3M+1
1
-M-1/2
0
-M
M+1/2


ZJ     +
CJ
-3M-5/2
3M-3
0
-M-1/2
0
0
2M+1/2
 
0
S1
16/3
0
7/2
0
-2/3
1
-1/6
2/3
32/21
2
X1
1/3
1
-1
0
1/3
0
1/3
-1/3
-
1
X3
2/3
0
1/2
1
-1/3
0
1/6
1/3
4/3

ZJ
4/3
2
-3/2
1
1/3
0
5/6
-1/3


ZJ     +
CJ
0
-11/2
0
1/3
0
M + 5/6
M – 1/3

0
S1
2/3
0
0
-7
5/3
1
-4/3
-5/3
2/5
2
X1
5/3
1
0
2
-1/3
0
2/3
1/3
-
4
X2
4/3
0
1
2
-2/3
0
1/3
2/3
-

ZJ
26/3
2
4
12
-10/3
0
8/3
10/3


ZJ     +
CJ
0
0
11
-10/3
0
M + 8/3
M + 10/3

0
S3
2/5
0
0
-21/5
1
-3/5
-4/5
-1
-
2
X1
9/5
1
0
3/5
0
1/5
2/5
0
3
4
X2
8/5
0
1
-4/5
0
2/5
-1/5
0
-

ZJ
10
2
4
-2
0
2
0
0


ZJ     +
CJ
0
0
-3
0
2
M
M

0
S3
13
7
0
0
8
2
2
-8

1
X3
3
5/3
0
1
0
1/3
2/3
0

4
X2
4
4/3
1
0
0
2/3
1/3
0


ZJ
19
7
4
1
0
3
2
0


ZJ     +
CJ
5
0
0
0
3
M + 2
M

X2 = 4        X3 = 3          S3 = 13       Z  =  19

Max Z  =  2(0) + 4(4) + 1(3) + 0(S1) + 0(13) – M(0) – M(0)  =  19
Max Z  =  19

11.-Max X        =  X1 + 2X2
            S.a.
                            X1 – 4X2  ≤  1
                        -3X1 + 2X2  ≤  6
                               X1 , X2  ≥  0
Forma Estandarizada:
            Max  Z  =  X1 + 2X2 + 0S1 + 0S2
S.a.
               X1 – 4X2 +0S1             =  1
            -3X1 +2X2           +0S2   =  6
                        X1 , X2 , S1 , S2   ≥  0








CJ
1
2
0
0

CB
XB
bi
X1
X2
S1
S2
θ K
0
S1
1
1
-4
1
0
-
0
S2
6
-3
2
0
1
3

ZJ
0
0
0
0
0


ZJ    +

CJ

-1
-2
0
0

0
S1
13
-5
0
1
2
-
2
X2
3
-3/2
1
0
1/2
-

ZJ
6
-3
2
0
1


ZJ   +

CJ

-4
0
0
1