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FECHA: 03/MARZO/2011
Práctica de programación lineal

1. Una compañía está planteando una campaña de publicidad con un presupuesto de $2, 500,000. Se contemplan dos medios: anuncios de $100,000 por radio o comerciales de $200,000 en T.V. Cada anuncio en la radio llega a una audiencia de 12,000 personas., cada comercial en T.V. lo ven 20,000 personas. La campaña quiere maximizar laaudiencia total, pero también está interesada por dos grupos específicos dentro de esa audiencia: mujeres entre los 21 y 35 años y hombres mayores de 40 años. Desea llegar por lo menos a 10,000 de estas mujeres y 8,028 de los hombres. Los medios de difusión proporcionaron los siguientes datos:
 Medio de Publicidad | Mujeres (21-35) | Hombres ≥ 40 |
Radio | 2,000 | 1,500 |
T.V. | 4,000 | 5,000 |¿Cómo se debe de gastar el presupuesto de publicidad?

Sea: X1=No.de comerciales por radio
X2=No.de comerciales en T.V.
Recursos | x1 | x2 | Magnitud |
Mujeres | 2,000 | 4,000 | 10,000 |
Hombres | 1,500 | 5,000 | 8,028 |
Presupuesto | 100,000 | 200,000 | 250,000 |
Audiencia | 12,000 | 20,000 | Max. |

Max f0=12,000x1+20,000x2
Mujeres | 2,000x1 | 4,000x2 | ≥10,000…-y1+R1 |
Hombres | 1,500x1 | 5,000x2 | ≥ 8,028…-y2+R2 |
Presupuesto | 100,000x1 | 200,000x1 | ≤ 250,000…+y3 |
Sujeta a:

Fase I
Min r0=∑Ri r0=R1,R2,R3 ; 0 = r0-R1-R2-R3

Iteración | V.B. | Valores | x1 | x2 | y1 | y2 | r0 | R1 | R2 | y3 | Relación |
  | r0  | 0 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 0 |   |
0 | R1  | 10,000 | 2,000 | 40,000 | -1 | 0 | 0 | 1 | 0 | 0 |   |
  |R2  | 8,028 | 1,500 | 5,000 | 0 | -1 | 0 | 0 | 1 | 0 |   |
  | y3  | 2,500,000 | 100,000 | 200,000 | 0 | 0 | 0 | 0 | 0 | 1 |   |
  | r0  | 18,028 | 3,500 | 9,000 | -1 | -1 | 1 | 0 | 0 | 0 |   |
1 | R1  | 10,000 | 2,000 | 4,000 | -1 | 0 | 0 | 1 | 0 | 0 | 2.5 |
e→x2 | R2  | 8,028 | 1,500 | 5,000 | 0 | -1 | 0 | 0 | 1 | 0 | 1.6 |
s→ R2 | y3  | 2,500,000 | 100,000 | 200,000 | 0 | 0 | 0 | 0 | 0| 1 | 12.5 |
  | r0  | 17,888/5 | 800 | 0 | -1 | 4/5 | 1 | 0 | -9/5 | 0 |   |
2 | R1  | 17,888/5 | 800 | 0 | -1 | 4/5 | 0 | 1 | -4/5 | 0 | 4.47 |
e→x1 | x2  | 2007/1250 |  3/10 | 1 | 0 | -1/5000 | 0 | 0 | 1/5000 | 0 | 5.35 |
s→ R1 | y3  | 2,178,880 | 40,000 | 0 | 0 | 40 | 0 | 0 | -40 | 1 | 54.47 |
  | r0  | 0 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 0 |   |
3 | x1  | 559/125 | 1 | 0 | -1/800| 1/1000 | 0 | 1/800 | -1/1000 | 0 |   |
  | x2  | 33/125 | 0 | 1 | 3/800 | -1/2000 | 0 | -3/8000 | 1/2000 | 0 |   |
  | y3  | 2,000,000 | 0 | 0 | 50 | 0 | 0 | -50 | 0 | 1 |   |

Operaciones Fase I:
r0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 0 |
R1 | 10,000 | 2,000 | 4,000 | -1 | 0 | 0 | 1 | 0 | 0 |
R2  | 8,028 | 1,500 | 5,000 | 0 | -1 | 0 | 0 | 1 | 0 |
r0 | 18,028 | 3,500 | 9,000 | -1| -1 | 1 | 0 | 0 | 0 |
| | | | | | | | | |
r0 | 18,028 | 3,500 | 9,000 | -1 | -1 | 1 | 0 | 0 | 0 |
x2  | -14450.4 | -2,700 | -9,000 | 0 |  9/5 | 0 | 0 | -9/5 | 0 |
r0 | 17,888/5 | 800 | 0 | -1 | 4/5 | 1 | 0 | -9/5 | 0 |
| | | | | | | | | |
R1 | 10,000 | 2,000 | 4,000 | -1 | 0 | 0 | 1 | 0 | 0 |
x2  |  -3,2122/5 | -1,200 | -4,000 | 0 | 4/5 | 0 | 0 | -4/5 | 0 |
R1| 17,888/5 | 800 | 0 | -1 | 4/5 | 0 | 1 | -4/5 | 0 |
| | | | | | | | | |
y3 | 2,500,000 | 100,000 | 200,000 | 0 | 0 | 0 | 0 | 0 | 1 |
x2  | -321,120 | -60,000 | -200,000 | 0 | 40 | 0 | 0 | -40 | 0 |
y3 | 2,178,880 | 40,000 | 0 | 0 | 40 | 0 | 0 | -40 | 1 |
| | | | | | | | | |
r0 | 17,888/5 | 800 | 0 | -1 | 4/5 | 1 | 0 | -9/5 | 0 |
x1  | -17,888/5 | -800 | 0 | 1 |-4/5 | 0 | -1 | 4/5 | 0 |
r0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 0 |
| | | | | | | | | |
x2 | 2007/1250 | 3/10 | 1 | 0 | -1/5000 | 0 | 0 | 1/5000 | 0 |
x1  | -1677/1250 | -3/10 | 0 | 3/8,000 | -3/10000  | 0 | -3/8000 | 3/10000 | 0 |
x2 | 33/125 | 0 | 1 | 3/8,000 | -1/200 | 0 | -3/8000 | 1/200 | 0 |
| | | | | | | | | |
y3 | 2,178,880 | 40,000 | 0 | 0 | 40 | 0...