metodo siemplex

1. Ejercicio 1.1
REQUERIMIENTO HORAS REQUERIMINETO HORAS HORAS DISPONIBLES MES
M1 M2
ESTRUCTURA PRINCIPAL 4 2 1600
ALAMBRADO ELECTRICO 2.5 1 1200
ENSAMBLADO 4.5 1.5 1600
BENEFICIO UNITARIO 40.00 10.00
X1: Número de equipos de prueba M1.
X2: Número de equipos de prueba M2.
Max Z = 40 X1 + 10 X2
s.a 4 X1 + 2 X2 <= 1600
2.5 X1 + 1 X2 <= 1200
4.5 X1 + 1.5 X2 <= 1600
Estándar:
Min Z = - 40 X1 - 10 X2 + 0 X3 + 0X4 + 0X5
4 X1 + 2 X2 + X3 = 1600
2.5 X1 + 1 X2 + X4 = 1200
4.5 X1 + 1.5 X2 + X5 = 1600
Canónico:
X1 X2 X3 X4 X5 Z
-40 -10 0 0 0 0
4 2 1 0 0 1600
2.5 1 0 1 0 1200
4.5 1.5 0 0 1 1600
X1 = X2 = 0 , X3 = 1600 , X4 = 1200 , X5 = 1600 , Z = 0
X1 X2 X3 X4 X5 Z
-40 -10 0 0 0 0
4 2 1 0 0 1600
5/2 1 0 1 0 1200
1 1/3 0 0 2/9 3200/9
X1 X2 X3 X4 X5 Z
0 10/3 0 0 80/9 128000/9
0 -2/3 -1 0 8/9 -1600/9
0 -1/6 0 -1 5/9 -2800/9
1 1/3 0 0 2/9 3200/9
X1 X2 X3 X4 X5 Z
0 10/3 0 0 80/9 128000/9
0 2/3 1 0 -8/9 1600/9
0 1/6 0 1 -5/9 2800/9
1 1/3 0 0 2/9 3200/9
Solución:
X1 = 3200/9 , X2 = 0 , X3 = 1600/9 , X4 = 2800/9 , X5 = 0 , Z = 128000/9

2. Ejercicio 1.3
X1: Número de cajas de tipo A a fabricar.
X2: Número de cajas de tipo B a fabricar.
Max Z = 120 X1 + 90 X2
s.a 0.3 X1 + 0.4 X2 <= 100
0.5 X1 + 0.2 X2 <= 120
0.2 X1 + 0.4 X2 <= 100
Estándar:
Min Z = - 120 X1 - 90 X2 + 0 X3 + 0X4 + 0X5
0.3 X1 + 0.4 X2 + X3 = 100
0.5 X1 + 0.2 X2 + X4 = 120
0.2 X1 + 0.4 X2 + X5 = 100
Canónico:
X1 X2 X3 X4 X5 Z
-120 -90 0 0 0 0
3/10 4/10 1 0 0 100
5/10 2/10 0 1 0 120
2/10 4/10 0 0 1 100
X1 = X2 = 0 , X3 = 100 , X4 = 120 , X5 = 100 , Z = 0
X1 X2 X3 X4 X5 Z
0 -42 0 240 0 28800
0 -7/25 -1 3/5 0 -28
1 2/5 0 10/5 0 240
0 -16/50 0 2/5 -1 -52
X1 X2 X3 X4 X5 Z
0 -42 0 240 0 28800
0 7/25 1 -3/5 0 28
1 2/5 0 10/5 0 240
0 16/50 0 -2/5 1 52
X1 X2 X3 X4 X5 Z
0 0 150 150 0 33000
0 1 25/7 -15/7 0 100
-1 0 10/7 -20/7 0 -200
0 0 8/7 -10/35 -1 -20
X1 X2 X3 X4 X5 Z
0 0 150 150 0 33000
0 1 25/7 -15/7 0 100
1 0 -10/7 20/7 0 200
0 0 -8/7 10/35 1 20
Solución:
X1 = 200 , X2 = 100 , X3 = 0 , X4 = 0 , X5 = 20 , Z = 33000
TIPO A TIPO B TOTAL
BOMBONES DE LICOR 0.30 Kgr. 0.40 Kgr. 100 Kgr.
BOMBONES DE NUEZ 0.50 Kgr. 0.20 Kgr. 120 Kgr.
BOMBONES DE FRUTA 0.20 Kgr. 0.40 Kgr. 100 Kgr.
UTILIDAD 120.00 90.00

3. Ejercicio 1.4
X1: Número de barriles de cerveza rubia a producir.
X2: Número de barriles de cerveza negra a producir.
Max Z = 5 X1 + 2 X2
s.a 5 X1 + 2 X2 <= 60
2 X1 + 1 X2 <= 25
Estándar:
Min Z = - 5 X1 - 2 X2 + 0 X3 + 0X4
5 X1 + 2 X2 + X3 = 60
2 X1 + 1 X2 + X4 = 25
Canónico:
X1 X2 X3 X4 Z
-5 -2 0 0 0
5 2 1 0 60
2 1 0 1 25
X1 = X2 = 0 , X3 = 60 , X4 = 25 , Z = 0
X1 X2 X3 X4 Z
-5 -2 0 0 0
1 2/5 1/5 0 12
2 1 0 1 25
X1 X2 X3 X4 Z
0 0 1 0 60
1 2/5 1/5 0 12
0 -1/5 2/5 -1 -1
X1 X2 X3 X4 Z
0 0 1 0 60
1 2/5 1/5 0 12
0 1/5 -2/5 1 1
Solución:
X1 = 12 , X2 = 0 , X3 = 0 , X4 = 1 , Z = 60
MAIZ LUPULO PRECIO
CERVEZA RUBIA 5 lb 2 lb 5.00
CERVEZA NEGRA 2 lb 1 lb 2.00
TOTAL 60 lb 25 lb

4. Ejercicio 1.5
X1: Número de tortas de chocolate a preparar.
X2: Número de tortas de vainilla a preparar.
Max Z = 1 X1 + 0.5 X2
s.a 1/3 X1 + 2/3 X2 <= 8
4 X1 + 1 X2 <= 30
Estándar:
Min Z = - 1 X1 – 0.5 X2 + 0 X3 + 0X4
1/3 X1 + 2/3 X2 + X3 = 8
4 X1 + 1 X2 + X4 = 30
Canónico:
X1 X2 X3 X4 Z
-1 -1/2 0 0 0
1/3 2/3 1 0 8
4 1 0 1 30
X1 = X2 = 0 , X3 = 8 , X4 = 30 , Z = 0
X1 X2 X3 X4 Z
-1 -1/2 0 0 0
1/3 2/3 1 0 8
1 1/4 0 1/4 30/4
X1 X2 X3 X4 Z
0 -1/4 0 1/4 30/4
0 -7/12 -1 1/12 -11/2
1 1/4 0 1/4 30/4
X1 X2 X3 X4 Z
0 -1/4 0 1/4 30/4
0 7/12 1 -1/12 11/2
1 1/4 0 1/4 30/4
X1 X2 X3 X4 Z
0 0 3/7 3/14 69/7
0 1 12/7 -1/7 66/7
-1 0 3/7 -2/7 -36/7
X1 X2 X3 X4 Z
0 0 3/7 3/14 69/7
0 1 12/7 -1/7 66/7
1 0 -3/7 2/7 36/7
Solución:
X1 = 36/7 , X2 = 66/7 , X3 = 0 , X4 = 0 , Z = 69/7
TIEMPO COCCION HUEVOS PRECIO
TORTA DE CHOCOLATE 1/3 hora 4 1.00
TORTA DE VAINILLA 2/3 hora 1 0.50
TOTAL 8 horas 30

5. Ejercicio 1.10
X1: Número de disposiciones tipo 1 a usar.
X2: Número de disposiciones tipo 2 a usar.
X3: Número de disposiciones tipo 3 a usar.
Max Z = 50 X1 + 30 X2 + 60 X3
s.a 30 X1 + 10 X2 + 20 X3 <= 1000
20 X1 + 40 X2 + 50 X3 <= 800
4 X1 + 3 X2 + 2 X3 <= 100
Estándar:
Min Z = - 50 X1 - 30 X2 - 60 X3 + 0X4 + 0X5 + 0 X6
30 X1 + 10 X2 + 20 X3 + X4 = 1000
20 X1 + 40 X2 + 50 X3 + X5 = 800
4 X1 + 3 X2 + 2 X3 + X6 = 100
Canónico:
X1 X2 X3 X4 X5 X6 Z
-50 -30 -60 0 0 0 0
30 10 20 1 0 0 1000
20 40 50 0 1 0 800
4 3 2 0 0 1 100
X1 = X2 = 0 , X3 = 0 , X4 = 1000 , X5 = 800 , X6 = 100 , Z = 0
X1 X2 X3 X4 X5 X6 Z
-26 18 0 0 6/5 0 960
-22 6 0 -1 2/5 0 -680
2/5 4/5 1 0 1/50 0 16
-16/5 -7/5 0 0 2/50 -1 -68
X1 X2 X3 X4 X5 X6 Z
-26 18 0 0 6/5 0 960
22 -6 0 1 -2/5 0 680
2/5 4/5 1 0 1/50 0 16
16/5 7/5 0 0 -2/50 1 68
X1 X2 X3 X4 X5 X6 Z
-26 18 0 0 6/5 0 960
22 -6 0 1 -2/5 0 680
2/5 4/5 1 0 1/50 0 16
1 7/16 0 0 -1/80 5/16 85/4
X1 X2 X3 X4 X5 X6 Z
0 235/8 0 0 35/40 65/8 3025/2
0 125/8 0 -1 5/40 55/8 -425/2
0 -25/40 -1 0 -5/200 1/8 -75/10
1 7/16 0 0 -1/80 5/16 85/4
TULIPANES ROSAS JAZMINES PRECIO
DISPOSICION 1 30 20 4 50.00
DISPOSICION 2 10 40 3 30.00
DISPOSICION 3 20 50 2 60.00
TOTAL 1000 800 100

6. X1 X2 X3 X4 X5 X6 Z
0 235/8 0 0 35/40 65/8 3025/2
0 -125/8 0 1 -5/40 -55/8 425/2
0 25/40 1 0 5/200 -1/8 75/10
1 7/16 0 0 -1/80 5/16 85/4
Solución:
X1 = 85/4 , X2 = 0 , X3 = 75/10 , X4 = 425/2 , X5 = 0 , X6 = 0 , Z = 3025/2