Investigacion De La Operacion

PROBLEMA 1
En una compañía Juan esta tratando de decidir cuantas amarras para trailer debe hacer de un metal de desperdicio tiene dos tipos de metal y puede ser cualquiera de dos tipos de ganchos en la tabla siguiente se proporcionan los datos necesarios:
Metal | Soldadura 1 | Soldadura 2 | disponible |
Hierro acanalado | 5 | 5 | 35 unidades |
Hierro plano | 6 | 9 | 54 unidades |

Juan gana$13 por cada gancho tipo 1 y $16 por cada gancho tipo 2 ya prometió hacer 2 ganchos del tipo 2
a) resuelve este problema por método simplex
b) le han prometido a Juan hierro acanalado adicional a $2 por unidad ¿deberá comprarlo?
z= 13x1+16x2+0S3+0S4+0S5-MA6 |
5X1+5X2+S3+0S4+0S5+0A6=35 |
6X1+9X2+0S3+S4+0S5+0A6=54 |
0X1+X2+0S3+0S4-S5+A6=2 |

| | CJ | 13 | 16 | 0 | 0 | 0 | -10 | |
CJ | MEZCLA| CANTIDAD | X1 | X2 | S3 | S4 | S5 | A6 | 35/5=7 |
0 | S3 | 35 | 5 | 5 | 1 | 0 | 0 | 0 | 54/9=6 |
0 | S4 | 54 | 6 | 9 | 0 | 1 | 0 | 0 | 2/1=2 |
-10 | A6 | 2 | 0 | 1 | 0 | 0 | -1 | 1 | |
  | ZJ | -20 | 0 | -10 | 0 | 0 | 10 | -10 | |
  | CJ-ZJ |   | 13 | 26 | 0 | 0 | -10 | 0 | |

| | CJ | 13 | 16 | 0 | 0 | 0 | -10 | |
CJ | MEZCLA | CANTIDAD | X1 | X2 | S3 | S4 | S5 | A6 | |
RN.0 | S3| 25 | 5 | 0 | 1 | 0 | 5 | -5 | 25/5=5 |
R.N.0 | S4 | 36 | 6 | 0 | 0 | 1 | 9 | -9 | 36/9=4 |
RR.-10 | X2 | 2 | 0 | 1 | 0 | 0 | -1 | 1 | 2/-1=-2 |
  | ZJ | 32 | 0 | 16 | 0 | 0 | -16 | 16 | |
  | CJ-ZJ |   | 13 | 0 | 0 | 0 | 16 | -26 | |

35-(5)(2) 54-(9)(2)
5-(5)(0) 6-(9)(0)
5-(5)(1) 9-(9)(1)
1-(5)(0) 0-(9)(0)
0-(5)(0) 1-(9)(0)
0-(5)(-1) 0-(9)(-1)
0-(5)(1) 0-(9)(1)
| | CJ | 13| 16 | 0 | 0 | 0 | -10 |
CJ | MEZCLA | CANTIDAD | X1 | X2 | S3 | S4 | S5 | A6 |
RN.0 | S3 | 5 | 5/3 | 0 | 1 | -5/9 | 0 | 0 |
R.R.0 | S5 | 4 | 6/9 | 0 | 0 | 1/9 | 1 | -1 |
16 | X2 | 6 | 2/3 | 1 | 0 | 1/9 | 0 | 0 |
  | ZJ | 96 | 32/3 | 16 | 0 | 16/9 | 0 | 0 |
  | CJ-ZJ |   | 7/3 | 0 | 0 | -16/9 | 0 | -10 |

25-(5)(4) 2-(-1)(4)
5-(5)(6/9) 0-(-1)(6/9)
0-(5)(0) 1-(-1)(0)
1-(5)(0)0-(-1)(0)
0-(5)(1/9) 0-(-1)(1/9)
5-(5)(1) -1-(-1)(1)
-5-(5)(-1) 1-(-1)(-1)
| | CJ | 13 | 16 | 0 | 0 | 0 | -10 |
CJ | MEZCLA | CANTIDAD | X1 | X2 | S3 | S4 | S5 | A6 |
RR.0 | X1 | 3 | 1 | 0 | 3/5 | -1/3 | 0 | 0 |
R.N.0 | S5 | 2 | 0 | 0 | -2/5 | 1/3 | 1 | -1 |
16 | X2 | 4 | 0 | 1 | -2/5 | 1/3 | 0 | 0 |
  | ZJ | 103 | 13 | 16 | 7/5 | 1 | 0 | 0 |
  | CJ-ZJ |   | 0 | 0 | -7/5 | -1 | 0 | -10|

4-(6/9)(3) 6-(2/3)(3)
6/9-(6/9)(1) 2/3-(2/3)(1)
0-(6/9)(0) 1-(2/3)(0)
0-(6/9)(3/5) 0-(2/3)(3/5)
1/9-(6/9)(3/5) 1/9-(2/3)(-1/3)
-1-(6/9)(0) 0-(2/3)(0)
1/9-(6/9)(0) 0-(2/3)(0)
PROBLEMA 2
MIN:
Z=4X1+6X2+4X3
SUJETO A: 3X1+X2+4X3>_36
2X1+4X2+X3>_40
Xi>_0,i=1,2,3
Z=4x1+6x2+4x3+0S4+0A5+0S6+MA7
3X1+X2+4X3-S4+A5+0S6+0A7=36
2X1+4X2+3X3+0S4+0A5-S6+A7=46
| | CJ | 4 | 6 | 4 | 0 |10 | 0 | 10 |
CJ | MEZCLA | CANTIDAD | X1 | X2 | X3 | S4 | A5 | S6 | A7 |
10 | A5 | 36 | 3 | 1 | 4 | -1 | 1 | 0 | 0 |
10 | A7 | 40 | 2 | 4 | 3 | 0 | 0 | -1 | 1 |
| ZJ | 760 | 50 | 50 | 70 | -10 | 10 | -10 | 10 |
| | | -46 | -44 | -66 | 10 | 0 | 10 | 0 |

| | CJ | 4 | 6 | 4 | 0 | 10 | 0 | 10 |
CJ | MEZCLA | CANTIDAD | X1 | X2 | X3 | S4 | A5 | S6 | A7 |
RR.4 | X3 | 9 | 3/4 | 1/4 | 1 |-1/4 | 1/4 | 0 | 0 |
RN.10 | A7 | 13 | -1/4 | 13/4 | 0 | 3/4 | -3/4 | -1 | 1 |
| ZJ | 166 | 1/2 | 67/2 | 4 | 13/2 | -13/2 | -10 | 10 |
| | | 7/2 | -55/2 | 0 | -13/2 | 33/2 | 10 | 0 |

40-(3)(9) 0-(3)(1/4)
2-(3)(3/4) -1-(3)(0)
4-(3)(1/4) 1-(3)(0)
3-(3)(1)
0-(3)(-1/4)
| | CJ | 4 | 6 | 4 | 0 | 10 | 0 | 10 |
CJ | MEZCLA | CANTIDAD | X1 | X2 | X3 | S4 | A5 | S6 | A7 |
RR.4 | X3 | 8 | 10/13| 0 | 1 | -11/13 | 4/13 | 1/13 | -1/3 |
RN.6 | X2 | 4 | -1/13 | 1 | 0 | 3/13 | -3/13 | -4/13 | 4/13 |
| ZJ | 56 | 34/13 | 6 | 4 | 2/13 | -2/13 | -20/13 | 20/13 |
| CJ-ZJ | | 18/13 | 0 | 0 | -2/13 | 132/13 | 20/13 | 10/13 |

9-(1/4)(4)
3/4-(1/4)(-1/13)
¼ -(1/4)(1)
1-(1/4)(0)
-1/4-(1/4)(-3/13)
¼-(1/4)(-3/13)
0-(1/4)(-4/13)
0-(1/4)(4/13)
| | CJ | 4 | 6 | 4 | 0 | 10 | 0 | 10 |
CJ...