Ejercicio De Investigacion De Operaciones

EJERCICIO DE INVESTIGACIÓN DE OPERACIONES
1. Minimizar:
C=0.60x+y
Sujeto a:
10x+4y≥20
5x + 5y ≥20
2x + 6y ≥12
x≥0 y≥0
Solución:
* USANDO PROLIN:F(0, 5) = 5; S S S
F(2, 0) = 1.2; S N N
F(0.666667, 3.333333) = 3.733333; S S S
F(1.384615, 1.538462) = 2.369231; S N S
F(0, 4) = 4; N S S
F(4,0) = 2.4; S S N
F(3, 1) = 2.8; S S S
F(0, 2) = 2; N N S
F(6, 0) = 3.6; S S S

Max(0, 5) = 5
Mín(3, 1) = 2.8
∴la respuesta para minimizar es:x=3
y=1
C= 2.8

x=3
y=1
C= 2.8

* USANDO SIMPLEX:
G=20u+20v+12w
Sujeto a:
10u+5v+2w≤0.6
4u +5v +6w≤1
u≥0 v≥0 w≥0

G-20u-20v-12w=010u+5v+2w+x=0.6
4u +5v +6w+y=1
G | U | V | W | X | Y | cte |
1 | -20 | -20 | -12 | 0 | 0 | 0 |
0 | 10 | 5 | 2 | 1 | 0 | 0.6 |
0 | 4 | 5 | 6 | 0 | 1 | 1 |

G | U | V | W| X | Y | cte | |
1 | -20 | -20 | -12 | 0 | 0 | 0 | 0-20 |
0 | 10 | 5 | 2 | 1 | 0 | 0.6 | 0.610 |
0 | 4 | 5 | 6 | 0 | 1 | 1 | 14 |

G | U | V | W | X | Y | cte ||
1 | 0 | -10 | -8 | 2 | 0 | 1.2 | -0.12 |
0 | 1 | 12 | 15 | 110 | 0 | 0.06 | 0.12 |
0 | 0 | 3 | 265 | -410 | 1 | 0.76 | 0.25 |

G | U | V | W | X | Y | cte | |1 | 20 | 0 | -4 | 4 | 0 | 2.4 | 0.6 |
0 | 2 | 1 | 25 | 15 | 0 | 0.12 | 0.3 |
0 | -6 | 0 | 4 | -1 | 1 | 0.4 | 0.1 |

G | U | V | W | X | Y | cte |
1 | 14 | 0 | 0| 3 | 1 | 2.8 |
0 | 135 | 1 | 0 | 310 | -110 | 0.16 |
0 | -32 | 0 | 1 | -14 | 14 | 0.1 |

∴la respuesta es:
x=3
y=1
C= 2.8

x=3
y=1
C= 2.8

* USANDOLINDO:
1. Indicamos la función objetivo y las restricciones a la cual está sujeto.
! FUNCION OBJETIVO
MAX 20U+20V+12W

SUBJECT TO
! RESTRICCIONES
X) 10U+5V+2W