simulacion_montecarlo2

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simulación de monteca PLANTEAMIENTO DEL PROBLEMA FAS 1) DEFINIR LAS VAR UNIDADES VEN PRECIO DE VE PRECIO DE CO 2) DEFINIR VARIABL COSTE DE TRA 3) DEFINIR VARIABL CANTIDAD A C 4) CALCULO DE LA F DE LAS VARIA 5) INTEGRACION DE COMBINAR LOS CON LA FUNCI Y SIMULAR LO TODAS LAS VA 6) FUNCION DE DIST COMO HERRAMI 7) COMPARACION DE OPTENCION DE PARA CADA CA COMO HERRAMI Unidades vendidas 20 10 21 20 22 30 23 30 24 20 25 10 El gerente de PRODUCTOS PRECEDEROS SL vende todos los días un producto perecedero en el mercado, de tal manera que las existencias que no se venden en el día constituyen una perdida neta igual al coste de su adquisición más 1€/unidad en concepto de transporte. A primera hora de la mañana adquiere las unidades de producto que prevé que va a vender. A continuación se va a su puesto en el mercado, donde permanece hasta las 14 horas. Después de esa hora las unidades sobrantes van al contenedor de basura. Por esta razón, el gerente desea ser muy cuidadoso con las provisiones de ese producto y con tal motivo ha decidido realizar un modelo de simulación que le informe de cuantas unidades de ese producto debe adquirir cada día. Si vende todo (COMPRAS <= DEMANDA) sus ingresos serán: (VENTAS x PRECIO DE VENTA) - (COMPRAS x PRECIO DE COMPRA) - (COMPRAS x 1 € de transporte) Si no vende todo, (COMPRAS > DEMANDA) sus ingresos serán: (DEMANDA x PRECIO DE VENTA) - (COMPRAS x PRECIO DE COMPRA) - (COMPRAS x 1€ de tansporte) Hay un coste de exceso si la DEMANDA < COMPRAS. La cantidad no vendida por el precio de compra más los gastos de transporte. Los datos históricos que puede facilitar son los siguientes: Nº de Los precios de venta han variado cada día y los datos que nos puede proporcionar son :

Transcript of simulacion_montecarlo2

Page 1: simulacion_montecarlo2

simulación de montecarlo con Excel

PLANTEAMIENTO DEL PROBLEMA FASES PARA DESARROLLAR EL MODELO:

1) DEFINIR LAS VARIABLES NO CONTROBLES (ALEATORIAS)UNIDADES VENDIDASPRECIO DE VENTAPRECIO DE COMPRA

2) DEFINIR VARIABLE NO CONTROLADAS DETERMINISTASCOSTE DE TRANSPORTE 1 € POR UNIDAD

3) DEFINIR VARIABLES CONTROLADAS CANTIDAD A COMPRAR ( 18, 19, 20, 21, 22, 23 …. ) a optimizar.

4) CALCULO DE LA FUNCION DE DISTRIBUCIONDE LAS VARIABLE NO CONTROLABLES (ALEATORIAS)

5) INTEGRACION DE LOS ELEMENTOS EN EL MODELOCOMBINAR LOS Nº ALEATORIOS OBTENIDOS CON EXCELCON LA FUNCION DE DISTRIBUCION VAR. ALEATORIASY SIMULAR LOS BENEFICIOS EN FUNCION DE LAS TODAS LAS VARIABLES DEL MODELO

6) FUNCION DE DISTRIBUCION DE LOS BENEFICIOS SIMULADOSCOMO HERRAMIENTA DE DECISIÓN

7) COMPARACION DE LOS BENEFICIOS ESPERADOSOPTENCION DE MEDIAS E INTERVALOS (nivel confianza 95 %)PARA CADA CANTIDAD COMPRADACOMO HERRAMIENTA DE DECISIÓN

Los datos históricos que puede facilitar son los siguientes:

Unidades vendidas Nº de días20 1021 2022 3023 3024 2025 10

El gerente de PRODUCTOS PRECEDEROS SL vende todos los días un producto perecedero en el mercado, de tal manera que las existencias que no se venden en el día constituyen una perdida neta igual al coste de su adquisición más 1€/unidad en concepto de transporte.

A primera hora de la mañana adquiere las unidades de producto que prevé que va a vender. A continuación se va a su puesto en el mercado, donde permanece hasta las 14 horas. Después de esa hora las unidades sobrantes van al contenedor de basura.

Por esta razón, el gerente desea ser muy cuidadoso con las provisiones de ese producto y con tal motivo ha decidido realizar un modelo de simulación que le informe de cuantas unidades de ese producto debe adquirir cada día.

Si vende todo (COMPRAS <= DEMANDA) sus ingresos serán: (VENTAS x PRECIO DE VENTA) - (COMPRAS x PRECIO DE COMPRA) - (COMPRAS x 1 € de transporte)

Si no vende todo, (COMPRAS > DEMANDA) sus ingresos serán: (DEMANDA x PRECIO DE VENTA) - (COMPRAS x PRECIO DE COMPRA) - (COMPRAS x 1€ de tansporte)

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Hay un coste de exceso si la DEMANDA < COMPRAS. La cantidad no vendida por el precio de compra más los gastos de transporte.

Los precios de venta han variado cada día y los datos que nos puede proporcionar son :

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Precio de venta Nº de días10 2012 3014 4016 3018 10

Precio de compra Nº de días5 157 259 3511 2517 10

Asimismo nos puede facilitar el precio de compra unitario de la mercancía

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simulación de montecarlo con Excel

FASES PARA DESARROLLAR EL MODELO:

1) DEFINIR LAS VARIABLES NO CONTROBLES (ALEATORIAS)

2) DEFINIR VARIABLE NO CONTROLADAS DETERMINISTASCOSTE DE TRANSPORTE 1 € POR UNIDAD

3) DEFINIR VARIABLES CONTROLADAS CANTIDAD A COMPRAR ( 18, 19, 20, 21, 22, 23 …. ) a optimizar.

4) CALCULO DE LA FUNCION DE DISTRIBUCIONDE LAS VARIABLE NO CONTROLABLES (ALEATORIAS)

5) INTEGRACION DE LOS ELEMENTOS EN EL MODELOCOMBINAR LOS Nº ALEATORIOS OBTENIDOS CON EXCELCON LA FUNCION DE DISTRIBUCION VAR. ALEATORIASY SIMULAR LOS BENEFICIOS EN FUNCION DE LAS TODAS LAS VARIABLES DEL MODELO

6) FUNCION DE DISTRIBUCION DE LOS BENEFICIOS SIMULADOSCOMO HERRAMIENTA DE DECISIÓN

7) COMPARACION DE LOS BENEFICIOS ESPERADOSOPTENCION DE MEDIAS E INTERVALOS (nivel confianza 95 %)PARA CADA CANTIDAD COMPRADACOMO HERRAMIENTA DE DECISIÓN

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Empresa: PRODUCTOS PERECEDEROS SL

1 - Variables no controlables aleatorias:

VENTAS PRECIO DE VENTA PRECIO DE COMPRAuds vendidas nº de días precios nº de días precios nº de días

20 10 10 20 5 1521 20 12 30 7 2522 30 14 40 9 3523 30 16 30 11 2524 20 18 10 17 1025 10

2 - Variables no controlables deterministas:

coste exceso = Precio adquisición + 1€

3 - Variables controlables:

cantidad de productos a adquirir: 18, 19, 20…. 30

4 - Distribución de probabilidad de las variables no controlables:

Demanda Precio venta Precio compraPr. Acumulada Demanda nº de días Pr. Suceso Pr. Acumulada P. Venta nº de días Pr. Suceso Pr. Acumulada P. Compra nº de días Pr. Suceso

0.00 19 0.00 9 0.00 40.08 20 10 0.08 0.15 10 20 0.15 0.14 5 15 0.140.25 21 20 0.17 0.38 12 30 0.23 0.36 7 25 0.230.50 22 30 0.25 0.69 14 40 0.31 0.68 9 35 0.320.75 23 30 0.25 0.92 16 30 0.23 0.91 11 25 0.230.92 24 20 0.17 1.00 18 10 0.08 1.00 17 10 0.091.00 25 10 0.08 130 1.00 110 1.00

120 1.00

A continuación se representa gráficamente el área de probabilidad de cada suceso:

5 - Integración de los elementos en el modelo

Objetivo: decidir el nº de unidades de máximo beneficio que debe adquirir la empresa PRODUCTOS PERECEDEROS SL

Método: simulación de Montecarlo con Excel = método cuantitativo que a partir de una muestra estadística y una serie de números aleatorios analiza el comportamiento de sistemas reales no dinámicos.

Modelo: Max Beneficio / Beneficio=si adquisición <= demanda, ((adquisición x precio de

venta) - (adquisición x precio de compra) - (adquisición x transporte)), (demanda x precio de venta) - (demanda x precio de compra) - (demanda x transporte) - coste de exceso) (utilizando notación Excel)

Se trata de generar una serie de números pseudo-aleatorios mediante Excel, dentro de una distribución uniforme entre 0 y 1, y buscar el intervalo de números aleatorios asociados a cada suceso a partir de la columna de probabilidad acumulada. Se realizan 1000 ensayos

Con los datos simulados se calcula el beneficio para las distintas cantidades a adquirir (variables controlables) y conforme a la fórmula del modelo.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.15

0.23

0.31

0.23

0.08

precio de venta

prob. precio vta. 10 prob. precio vta. 12 prob. precio vta. 14

prob. precio vta.16 prob. precio vta. 18

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.08

0.17

0.25

0.25

0.17

0.08

demanda

prob. Demanda 20 uds prob. Demanda 21 uds

prob. Demanda 22 uds prob. Demanda 23 uds

prob. Demanda 24 uds prob. Demanda 25 uds

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.14

0.23

0.32

0.23

0.09

precio de compra

prob. precio compra 5 prob. precio compra 7

prob. precio compra 9 prob. precio compra 11

prob. precio compra 17

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ASIGNACIÓN DE SUCESOS A LOS NUM. ALEATORIOS EXCELSIMULACIÓN DE BENEFICIOS PARA LAS SIGUIENTES CANTIDADES A COMPRAR

18 19 20 21 22 23 24 25 26nº sucesos demanda precio venta precio compra coste compra coste exceso beneficios coste exceso beneficios coste exceso beneficios coste exceso beneficios coste exceso beneficios coste exceso beneficios coste exceso beneficios coste exceso beneficios coste exceso beneficios

1 23 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 7 223 14 216 21 2092 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 713 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 394 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -565 25 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 9 1416 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 657 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 658 21 17 6 7 0 180 0 190 0 200 0 210 7 203 14 196 21 189 28 182 35 1759 20 15 12 13 0 36 0 38 0 40 13 27 26 14 39 1 52 -12 65 -25 78 -38

10 23 10 12 13 0 -54 0 -57 0 -60 0 -63 0 -66 0 -69 13 -82 26 -95 39 -10811 22 15 12 13 0 36 0 38 0 40 0 42 0 44 13 31 26 18 39 5 52 -812 21 17 10 11 0 108 0 114 0 120 0 126 11 115 22 104 33 93 44 82 55 7113 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 814 25 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 6 9415 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -316 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 7117 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 15718 22 11 6 7 0 72 0 76 0 80 0 84 0 88 7 81 14 74 21 67 28 6019 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 1920 21 11 12 13 0 -36 0 -38 0 -40 0 -42 13 -55 26 -68 39 -81 52 -94 65 -10721 25 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 7 14322 20 15 6 7 0 144 0 152 0 160 7 153 14 146 21 139 28 132 35 125 42 11823 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 4824 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -5625 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 1926 21 10 6 7 0 54 0 57 0 60 0 63 7 56 14 49 21 42 28 35 35 2827 22 10 12 13 0 -54 0 -57 0 -60 0 -63 0 -66 13 -79 26 -92 39 -105 52 -11828 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 11729 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 13330 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -6631 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -2432 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -4633 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 13334 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 5935 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 9136 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 13037 25 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 9 19138 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11139 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11140 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 8141 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 15742 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 13043 21 10 10 11 0 -18 0 -19 0 -20 0 -21 11 -32 22 -43 33 -54 44 -65 55 -7644 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 15745 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -1346 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 3047 21 11 6 7 0 72 0 76 0 80 0 84 7 77 14 70 21 63 28 56 35 4948 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 6549 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -2650 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 17851 25 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 0 75 7 6852 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 13053 21 11 12 13 0 -36 0 -38 0 -40 0 -42 13 -55 26 -68 39 -81 52 -94 65 -10754 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11155 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 14856 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 17857 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 858 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 10459 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 7860 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 9161 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 16362 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 9163 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 1364 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 14365 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -2666 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -4667 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 9168 20 13 12 13 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52 65 -65 78 -7869 23 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 6 201 12 195 18 18970 22 17 5 6 0 198 0 209 0 220 0 231 0 242 6 236 12 230 18 224 24 21871 24 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 6 114 12 10872 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -5573 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 5974 24 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 0 -48 13 -61 26 -7475 22 17 10 11 0 108 0 114 0 120 0 126 0 132 11 121 22 110 33 99 44 8876 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 16377 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 11778 24 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 0 -48 13 -61 26 -7479 23 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 13 -59 26 -72 39 -8580 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 59

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81 20 15 10 11 0 72 0 76 0 80 11 69 22 58 33 47 44 36 55 25 66 1482 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -5583 20 15 8 9 0 108 0 114 0 120 9 111 18 102 27 93 36 84 45 75 54 6684 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 1385 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 13086 24 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 11 37 22 2687 20 15 12 13 0 36 0 38 0 40 13 27 26 14 39 1 52 -12 65 -25 78 -3888 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 3089 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 14890 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 10491 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 7492 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 8193 22 10 6 7 0 54 0 57 0 60 0 63 0 66 7 59 14 52 21 45 28 3894 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -3395 22 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 13 -57 26 -70 39 -83 52 -9696 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 897 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11198 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 5999 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 74

100 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178101 24 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 0 168 6 162 12 156102 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0103 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96104 22 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 13 -57 26 -70 39 -83 52 -96105 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -24106 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130107 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55108 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96109 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19110 20 13 8 9 0 72 0 76 0 80 9 71 18 62 27 53 36 44 45 35 54 26111 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 93112 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143113 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13114 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52115 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130116 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30117 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39118 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81119 23 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 6 201 12 195 18 189120 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22121 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52122 20 11 6 7 0 72 0 76 0 80 7 73 14 66 21 59 28 52 35 45 42 38123 25 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 9 41124 22 10 5 6 0 72 0 76 0 80 0 84 0 88 6 82 12 76 18 70 24 64125 20 15 8 9 0 108 0 114 0 120 9 111 18 102 27 93 36 84 45 75 54 66126 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 74127 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55128 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52129 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148130 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33131 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81132 20 10 5 6 0 72 0 76 0 80 6 74 12 68 18 62 24 56 30 50 36 44133 23 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 13 33 26 20 39 7134 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22135 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33136 25 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 9 41137 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19138 23 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 13 33 26 20 39 7139 25 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11140 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65141 25 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 0 25 9 16142 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29143 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14144 23 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 13 -59 26 -72 39 -85145 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178146 22 17 8 9 0 144 0 152 0 160 0 168 0 176 9 167 18 158 27 149 36 140147 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 91148 21 10 6 7 0 54 0 57 0 60 0 63 7 56 14 49 21 42 28 35 35 28149 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52150 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19151 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104152 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13153 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14154 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13155 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117156 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 82157 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 117158 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111159 23 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 6 86 12 80 18 74160 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0161 22 11 5 6 0 90 0 95 0 100 0 105 0 110 6 104 12 98 18 92 24 86162 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78163 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13164 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104

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753 25 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 0 168 0 175 6 169754 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22755 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130756 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78757 25 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 0 168 0 175 6 169758 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30759 24 17 5 6 0 198 0 209 0 220 0 231 0 242 0 253 0 264 6 258 12 252760 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13761 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 157762 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96763 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56764 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 48765 20 15 8 9 0 108 0 114 0 120 9 111 18 102 27 93 36 84 45 75 54 66766 23 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 6 109 12 103 18 97767 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30768 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52769 24 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 0 -48 13 -61 26 -74770 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65771 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44772 20 13 10 11 0 36 0 38 0 40 11 29 22 18 33 7 44 -4 55 -15 66 -26773 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66774 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39775 20 10 6 7 0 54 0 57 0 60 7 53 14 46 21 39 28 32 35 25 42 18776 21 10 5 6 0 72 0 76 0 80 0 84 6 78 12 72 18 66 24 60 30 54777 25 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 7 143778 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 117779 24 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 9 15 18 6780 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 157781 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 82782 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143783 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39784 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96785 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13786 21 10 6 7 0 54 0 57 0 60 0 63 7 56 14 49 21 42 28 35 35 28787 21 13 12 13 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52 65 -65788 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 157789 20 11 5 6 0 90 0 95 0 100 6 94 12 88 18 82 24 76 30 70 36 64790 23 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 13 33 26 20 39 7791 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 91792 20 13 10 11 0 36 0 38 0 40 11 29 22 18 33 7 44 -4 55 -15 66 -26793 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3794 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130795 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65796 21 11 6 7 0 72 0 76 0 80 0 84 7 77 14 70 21 63 28 56 35 49797 20 11 8 9 0 36 0 38 0 40 9 31 18 22 27 13 36 4 45 -5 54 -14798 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117799 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4800 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66801 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 91802 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52803 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65804 25 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 9 141805 22 17 5 6 0 198 0 209 0 220 0 231 0 242 6 236 12 230 18 224 24 218806 23 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 6 109 12 103 18 97807 20 10 8 9 0 18 0 19 0 20 9 11 18 2 27 -7 36 -16 45 -25 54 -34808 24 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 0 192 9 183 18 174809 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81810 23 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 6 86 12 80 18 74811 23 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 6 109 12 103 18 97812 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78813 25 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 0 216 0 225 6 219814 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 59815 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89816 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29817 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29818 25 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 7 143819 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33820 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117821 22 17 6 7 0 180 0 190 0 200 0 210 0 220 7 213 14 206 21 199 28 192822 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52823 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71824 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44825 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111826 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 59827 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29828 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52829 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71830 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -24831 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33832 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44833 24 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 0 96 6 90 12 84834 24 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 11 37 22 26835 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30836 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56

Page 15: simulacion_montecarlo2

837 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104838 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71839 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -46840 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111841 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29842 21 17 6 7 0 180 0 190 0 200 0 210 7 203 14 196 21 189 28 182 35 175843 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 91844 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0845 23 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 13 -59 26 -72 39 -85846 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96847 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96848 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130849 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19850 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52851 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130852 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 157853 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89854 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52855 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104856 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 44857 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143858 22 17 5 6 0 198 0 209 0 220 0 231 0 242 6 236 12 230 18 224 24 218859 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71860 25 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 11 39861 21 15 5 6 0 162 0 171 0 180 0 189 6 183 12 177 18 171 24 165 30 159862 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19863 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81864 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104865 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65866 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55867 20 13 6 7 0 108 0 114 0 120 7 113 14 106 21 99 28 92 35 85 42 78868 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65869 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29870 24 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 11 37 22 26871 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81872 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178873 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 126874 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117875 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 44876 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39877 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81878 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55879 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52880 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55881 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4882 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 93883 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117884 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8885 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56886 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148887 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19888 21 11 5 6 0 90 0 95 0 100 0 105 6 99 12 93 18 87 24 81 30 75889 24 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 7 233 14 226890 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 157891 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 82892 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13893 20 10 10 11 0 -18 0 -19 0 -20 11 -31 22 -42 33 -53 44 -64 55 -75 66 -86894 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -46895 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 133896 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143897 21 10 10 11 0 -18 0 -19 0 -20 0 -21 11 -32 22 -43 33 -54 44 -65 55 -76898 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22899 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30900 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148901 20 15 10 11 0 72 0 76 0 80 11 69 22 58 33 47 44 36 55 25 66 14902 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3903 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33904 25 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 9 41905 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8906 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65907 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4908 25 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 0 75 7 68909 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13910 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81911 25 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 0 250 7 243912 24 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 0 192 9 183 18 174913 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33914 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26915 22 15 12 13 0 36 0 38 0 40 0 42 0 44 13 31 26 18 39 5 52 -8916 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56917 24 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 6 114 12 108918 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111919 22 15 5 6 0 162 0 171 0 180 0 189 0 198 6 192 12 186 18 180 24 174920 20 13 8 9 0 72 0 76 0 80 9 71 18 62 27 53 36 44 45 35 54 26

Page 16: simulacion_montecarlo2

921 20 10 5 6 0 72 0 76 0 80 6 74 12 68 18 62 24 56 30 50 36 44922 22 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 13 -57 26 -70 39 -83 52 -96923 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0924 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4925 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 126926 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 44927 20 13 10 11 0 36 0 38 0 40 11 29 22 18 33 7 44 -4 55 -15 66 -26928 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -24929 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104930 24 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 7 65 14 58931 21 17 6 7 0 180 0 190 0 200 0 210 7 203 14 196 21 189 28 182 35 175932 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56933 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39934 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33935 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52936 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19937 24 17 5 6 0 198 0 209 0 220 0 231 0 242 0 253 0 264 6 258 12 252938 20 13 5 6 0 126 0 133 0 140 6 134 12 128 18 122 24 116 30 110 36 104939 20 15 8 9 0 108 0 114 0 120 9 111 18 102 27 93 36 84 45 75 54 66940 24 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 9 15 18 6941 24 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 9 15 18 6942 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13943 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111944 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96945 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 133946 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30947 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22948 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 91949 22 11 6 7 0 72 0 76 0 80 0 84 0 88 7 81 14 74 21 67 28 60950 22 17 8 9 0 144 0 152 0 160 0 168 0 176 9 167 18 158 27 149 36 140951 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178952 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96953 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3954 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39955 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 74956 24 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 6 114 12 108957 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148958 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52959 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55960 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 74961 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143962 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148963 23 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 13 -59 26 -72 39 -85964 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66965 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 44966 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52967 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52968 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81969 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13970 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52971 25 17 12 13 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 13 87972 23 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 6 86 12 80 18 74973 22 15 12 13 0 36 0 38 0 40 0 42 0 44 13 31 26 18 39 5 52 -8974 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65975 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78976 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22977 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96978 22 15 12 13 0 36 0 38 0 40 0 42 0 44 13 31 26 18 39 5 52 -8979 23 17 12 13 0 72 0 76 0 80 0 84 0 88 0 92 13 79 26 66 39 53980 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4981 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178982 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178983 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 178984 23 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 6 109 12 103 18 97985 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65986 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65987 24 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 6 114 12 108988 20 15 10 11 0 72 0 76 0 80 11 69 22 58 33 47 44 36 55 25 66 14989 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 48990 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4991 20 11 8 9 0 36 0 38 0 40 9 31 18 22 27 13 36 4 45 -5 54 -14992 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96993 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78994 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0995 23 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 13 33 26 20 39 7996 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71997 20 13 8 9 0 72 0 76 0 80 9 71 18 62 27 53 36 44 45 35 54 26998 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14999 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22

1000 21 11 12 13 0 -36 0 -38 0 -40 0 -42 13 -55 26 -68 39 -81 52 -94 65 -107

Page 17: simulacion_montecarlo2

6 - Función de distribución de beneficios simulados:

20 unid. 22 unid. 24 unid.nº sucesos prob prob acum nº sucesos prob prob acum. nº sucesos prob prob acum

-114 0 0 0 0 0 0 0 0 0

-113 0 0 0 0 0 0 0 0 0

-112 0 0 0 0 0 0 1 0.002 0.002

-111 0 0 0 0 0 0 0 0 0.002

-110 0 0 0 0 0 0 0 0 0.002

-109 0 0 0 0 0 0 0 0 0.002

-108 0 0 0 0 0 0 0 0 0.002

-107 0 0 0 0 0 0 0 0 0.002

-106 0 0 0 0 0 0 0 0 0.002

-105 0 0 0 0 0 0 0 0 0.002

-104 0 0 0 0 0 0 0 0 0.002

-103 0 0 0 0 0 0 0 0 0.002

-102 0 0 0 0 0 0 0 0 0.002

-101 0 0 0 0 0 0 0 0 0.002

-100 0 0 0 0 0 0 0 0 0.002

-99 0 0 0 0 0 0 0 0 0.002

-98 0 0 0 0 0 0 0 0 0.002

-97 0 0 0 0 0 0 0 0 0.002

-96 0 0 0 0 0 0 0 0 0.002

-95 0 0 0 0 0 0 0 0 0.002

-94 0 0 0 0 0 0 0 0 0.002

-93 0 0 0 0 0 0 0 0 0.002

-92 0 0 0 0 0 0 2 0.004 0.006

-91 0 0 0 0 0 0 0 0 0.006

-90 0 0 0 0 0 0 0 0 0.006

-89 0 0 0 0 0 0 0 0 0.006

-88 0 0 0 0 0 0 0 0 0.006

-87 0 0 0 0 0 0 0 0 0.006

-86 0 0 0 1 0.002 0.002 0 0 0.006

-85 0 0 0 0 0 0.002 0 0 0.006

-84 0 0 0 0 0 0.002 0 0 0.006

-83 0 0 0 0 0 0.002 0 0 0.006

-82 0 0 0 0 0 0.002 1 0.002 0.008

-81 0 0 0 0 0 0.002 3 0.006 0.014

-80 0 0 0 0 0 0.002 0 0 0.014

Para comparar, de las 9 simulaciones realizadas, se eligen 3 ( 20, 22 y 24 unidades), se calcula la distribución de beneficios y se representa gráficamente la probabilidad acumulada.

-114

-113

-112

-111

-110

-109

-108

-107

-106

-105

-104

-103

-102

-101

-100 -99

-98

-97

-96

-95

-94

-93

-92

-91

-90

-89

-88

-87

-86

-85

-84

-83

-82

-81

-80

-79

-78

-77

-76

-75

-74

-73

-72

-71

-70

-69

-68

-67

-66

-65

-64

-63

-62

-61

-60

-59

-58

-57

-56

-55

-54

-53

-52

-51

-50

-49

-48

-47

-46

-45

-44

-43

-42

-41

-40

-39

-38

-37

-36

-35

-34

-33

-32

-31

-30

-29

-28

-27

-26

-25

-24

-23

-22

-21

-20

-19

-18

-17

-16

-15

-14

-13

-12

-11

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DISTRIBUCIÓN DE BENEFICIOS

20 unid.

22 unid.

24 unid.

BENEFICIO SIMULADO

PR

OB

. AC

UM

UL

AD

A

Page 18: simulacion_montecarlo2

-79 0 0 0 0 0 0.002 0 0 0.014

-78 0 0 0 0 0 0.002 0 0 0.014

-77 0 0 0 0 0 0.002 0 0 0.014

-76 0 0 0 0 0 0.002 0 0 0.014

-75 0 0 0 0 0 0.002 0 0 0.014

-74 0 0 0 0 0 0.002 0 0 0.014

-73 0 0 0 0 0 0.002 0 0 0.014

-72 0 0 0 0 0 0.002 3 0.006 0.02

-71 0 0 0 0 0 0.002 0 0 0.02

-70 0 0 0 0 0 0.002 3 0.006 0.026

-69 0 0 0 0 0 0.002 0 0 0.026

-68 0 0 0 0 0 0.002 0 0 0.026

-67 0 0 0 0 0 0.002 0 0 0.026

-66 0 0 0 6 0.012 0.014 0 0 0.026

-65 0 0 0 0 0 0.014 0 0 0.026

-64 0 0 0 0 0 0.014 1 0.002 0.028

-63 0 0 0 0 0 0.014 0 0 0.028

-62 0 0 0 0 0 0.014 0 0 0.028

-61 0 0 0 0 0 0.014 0 0 0.028

-60 7 0.014 0.014 0 0 0.014 0 0 0.028

-59 0 0 0.014 0 0 0.014 2 0.004 0.032

-58 0 0 0.014 0 0 0.014 0 0 0.032

-57 0 0 0.014 0 0 0.014 0 0 0.032

-56 0 0 0.014 0 0 0.014 0 0 0.032

-55 0 0 0.014 3 0.006 0.02 0 0 0.032

-54 0 0 0.014 0 0 0.02 4 0.008 0.04

-53 0 0 0.014 0 0 0.02 0 0 0.04

-52 0 0 0.014 0 0 0.02 1 0.002 0.042

-51 0 0 0.014 0 0 0.02 0 0 0.042

-50 0 0 0.014 0 0 0.02 0 0 0.042

-49 0 0 0.014 0 0 0.02 0 0 0.042

-48 0 0 0.014 0 0 0.02 2 0.004 0.046

-47 0 0 0.014 0 0 0.02 0 0 0.046

-46 0 0 0.014 0 0 0.02 0 0 0.046

-45 0 0 0.014 0 0 0.02 0 0 0.046

-44 0 0 0.014 7 0.014 0.034 7 0.014 0.06

-43 0 0 0.014 0 0 0.034 0 0 0.06

-42 0 0 0.014 1 0.002 0.036 0 0 0.06

-41 0 0 0.014 0 0 0.036 0 0 0.06

-40 10 0.02 0.034 0 0 0.036 0 0 0.06

-39 0 0 0.034 0 0 0.036 4 0.008 0.068

-38 0 0 0.034 0 0 0.036 0 0 0.068

-37 0 0 0.034 0 0 0.036 0 0 0.068

-36 0 0 0.034 0 0 0.036 0 0 0.068

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-35 0 0 0.034 0 0 0.036 0 0 0.068

-34 0 0 0.034 0 0 0.036 4 0.008 0.076

-33 0 0 0.034 0 0 0.036 8 0.016 0.092

-32 0 0 0.034 4 0.008 0.044 0 0 0.092

-31 0 0 0.034 0 0 0.044 0 0 0.092

-30 0 0 0.034 0 0 0.044 0 0 0.092

-29 0 0 0.034 0 0 0.044 0 0 0.092

-28 0 0 0.034 0 0 0.044 0 0 0.092

-27 0 0 0.034 0 0 0.044 0 0 0.092

-26 0 0 0.034 1 0.002 0.046 6 0.012 0.104

-25 0 0 0.034 0 0 0.046 0 0 0.104

-24 0 0 0.034 0 0 0.046 4 0.008 0.112

-23 0 0 0.034 0 0 0.046 0 0 0.112

-22 0 0 0.034 15 0.03 0.076 5 0.01 0.122

-21 0 0 0.034 0 0 0.076 0 0 0.122

-20 19 0.038 0.072 0 0 0.076 0 0 0.122

-19 0 0 0.072 0 0 0.076 0 0 0.122

-18 0 0 0.072 0 0 0.076 0 0 0.122

-17 0 0 0.072 0 0 0.076 0 0 0.122

-16 0 0 0.072 0 0 0.076 0 0 0.122

-15 0 0 0.072 0 0 0.076 0 0 0.122

-14 0 0 0.072 0 0 0.076 0 0 0.122

-13 0 0 0.072 4 0.008 0.084 2 0.004 0.126

-12 0 0 0.072 0 0 0.084 2 0.004 0.13

-11 0 0 0.072 8 0.016 0.1 12 0.024 0.154

-10 0 0 0.072 0 0 0.1 0 0 0.154

-9 0 0 0.072 0 0 0.1 0 0 0.154

-8 0 0 0.072 0 0 0.1 0 0 0.154

-7 0 0 0.072 0 0 0.1 0 0 0.154

-6 0 0 0.072 0 0 0.1 3 0.006 0.16

-5 0 0 0.072 0 0 0.1 0 0 0.16

-4 0 0 0.072 0 0 0.1 1 0.002 0.162

-3 0 0 0.072 0 0 0.1 0 0 0.162

-2 0 0 0.072 0 0 0.1 0 0 0.162

-1 0 0 0.072 0 0 0.1 0 0 0.162

0 54 0.108 0.18 40 0.08 0.18 15 0.03 0.192

1 0 0 0.18 0 0 0.18 0 0 0.192

2 0 0 0.18 0 0 0.18 0 0 0.192

3 0 0 0.18 0 0 0.18 2 0.004 0.196

4 0 0 0.18 0 0 0.18 5 0.01 0.206

5 0 0 0.18 0 0 0.18 0 0 0.206

6 0 0 0.18 0 0 0.18 0 0 0.206

7 0 0 0.18 0 0 0.18 0 0 0.206

8 0 0 0.18 0 0 0.18 0 0 0.206

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9 0 0 0.18 0 0 0.18 7 0.014 0.22

10 0 0 0.18 0 0 0.18 0 0 0.22

11 0 0 0.18 0 0 0.18 0 0 0.22

12 0 0 0.18 3 0.006 0.186 0 0 0.22

13 0 0 0.18 0 0 0.186 0 0 0.22

14 0 0 0.18 2 0.004 0.19 6 0.012 0.232

15 0 0 0.18 0 0 0.19 5 0.01 0.242

16 0 0 0.18 0 0 0.19 0 0 0.242

17 0 0 0.18 0 0 0.19 0 0 0.242

18 0 0 0.18 1 0.002 0.192 2 0.004 0.246

19 0 0 0.18 0 0 0.192 0 0 0.246

20 18 0.036 0.216 0 0 0.192 0 0 0.246

21 0 0 0.216 0 0 0.192 0 0 0.246

22 0 0 0.216 16 0.032 0.224 8 0.016 0.262

23 0 0 0.216 0 0 0.224 0 0 0.262

24 0 0 0.216 0 0 0.224 5 0.01 0.272

25 0 0 0.216 0 0 0.224 0 0 0.272

26 0 0 0.216 0 0 0.224 7 0.014 0.286

27 0 0 0.216 0 0 0.224 0 0 0.286

28 0 0 0.216 0 0 0.224 0 0 0.286

29 0 0 0.216 2 0.004 0.228 0 0 0.286

30 0 0 0.216 0 0 0.228 0 0 0.286

31 0 0 0.216 7 0.014 0.242 0 0 0.286

32 0 0 0.216 0 0 0.242 2 0.004 0.29

33 0 0 0.216 5 0.01 0.252 2 0.004 0.294

34 0 0 0.216 0 0 0.252 0 0 0.294

35 0 0 0.216 0 0 0.252 9 0.018 0.312

36 0 0 0.216 0 0 0.252 3 0.006 0.318

37 0 0 0.216 0 0 0.252 12 0.024 0.342

38 0 0 0.216 0 0 0.252 0 0 0.342

39 0 0 0.216 0 0 0.252 0 0 0.342

40 80 0.16 0.376 0 0 0.252 0 0 0.342

41 0 0 0.376 0 0 0.252 0 0 0.342

42 0 0 0.376 0 0 0.252 4 0.008 0.35

43 0 0 0.376 0 0 0.252 0 0 0.35

44 0 0 0.376 62 0.124 0.376 2 0.004 0.354

45 0 0 0.376 0 0 0.376 0 0 0.354

46 0 0 0.376 2 0.004 0.38 0 0 0.354

47 0 0 0.376 0 0 0.38 0 0 0.354

48 0 0 0.376 0 0 0.38 22 0.044 0.398

49 0 0 0.376 0 0 0.38 0 0 0.398

50 0 0 0.376 0 0 0.38 0 0 0.398

51 0 0 0.376 0 0 0.38 3 0.006 0.404

52 0 0 0.376 0 0 0.38 5 0.01 0.414

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53 0 0 0.376 0 0 0.38 0 0 0.414

54 0 0 0.376 0 0 0.38 0 0 0.414

55 0 0 0.376 0 0 0.38 0 0 0.414

56 0 0 0.376 4 0.008 0.388 1 0.002 0.416

57 0 0 0.376 0 0 0.388 10 0.02 0.436

58 0 0 0.376 3 0.006 0.394 0 0 0.436

59 0 0 0.376 0 0 0.394 0 0 0.436

60 17 0.034 0.41 0 0 0.394 0 0 0.436

61 0 0 0.41 0 0 0.394 0 0 0.436

62 0 0 0.41 2 0.004 0.398 5 0.01 0.446

63 0 0 0.41 0 0 0.398 4 0.008 0.454

64 0 0 0.41 0 0 0.398 0 0 0.454

65 0 0 0.41 0 0 0.398 0 0 0.454

66 0 0 0.41 12 0.024 0.422 7 0.014 0.468

67 0 0 0.41 0 0 0.422 0 0 0.468

68 0 0 0.41 1 0.002 0.424 0 0 0.468

69 0 0 0.41 0 0 0.424 0 0 0.468

70 0 0 0.41 0 0 0.424 13 0.026 0.494

71 0 0 0.41 0 0 0.424 0 0 0.494

72 0 0 0.41 0 0 0.424 2 0.004 0.498

73 0 0 0.41 3 0.006 0.43 0 0 0.498

74 0 0 0.41 0 0 0.43 4 0.008 0.506

75 0 0 0.41 10 0.02 0.45 0 0 0.506

76 0 0 0.41 0 0 0.45 7 0.014 0.52

77 0 0 0.41 4 0.008 0.458 0 0 0.52

78 0 0 0.41 3 0.006 0.464 0 0 0.52

79 0 0 0.41 0 0 0.464 1 0.002 0.522

80 108 0.216 0.626 0 0 0.464 0 0 0.522

81 0 0 0.626 0 0 0.464 10 0.02 0.542

82 0 0 0.626 0 0 0.464 0 0 0.542

83 0 0 0.626 0 0 0.464 12 0.024 0.566

84 0 0 0.626 0 0 0.464 4 0.008 0.574

85 0 0 0.626 0 0 0.464 5 0.01 0.584

86 0 0 0.626 0 0 0.464 3 0.006 0.59

87 0 0 0.626 0 0 0.464 3 0.006 0.596

88 0 0 0.626 82 0.164 0.628 0 0 0.596

89 0 0 0.626 0 0 0.628 0 0 0.596

90 0 0 0.626 0 0 0.628 0 0 0.596

91 0 0 0.626 0 0 0.628 0 0 0.596

92 0 0 0.626 0 0 0.628 1 0.002 0.598

93 0 0 0.626 0 0 0.628 1 0.002 0.6

94 0 0 0.626 0 0 0.628 0 0 0.6

95 0 0 0.626 0 0 0.628 0 0 0.6

96 0 0 0.626 0 0 0.628 24 0.048 0.648

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97 0 0 0.626 0 0 0.628 0 0 0.648

98 0 0 0.626 1 0.002 0.63 2 0.004 0.652

99 0 0 0.626 3 0.006 0.636 11 0.022 0.674

100 14 0.028 0.654 0 0 0.636 0 0 0.674

101 0 0 0.654 0 0 0.636 0 0 0.674

102 0 0 0.654 4 0.008 0.644 0 0 0.674

103 0 0 0.654 0 0 0.644 0 0 0.674

104 0 0 0.654 0 0 0.644 0 0 0.674

105 0 0 0.654 0 0 0.644 10 0.02 0.694

106 0 0 0.654 1 0.002 0.646 0 0 0.694

107 0 0 0.654 0 0 0.646 0 0 0.694

108 0 0 0.654 0 0 0.646 0 0 0.694

109 0 0 0.654 0 0 0.646 2 0.004 0.698

110 0 0 0.654 10 0.02 0.666 3 0.006 0.704

111 0 0 0.654 0 0 0.666 0 0 0.704

112 0 0 0.654 0 0 0.666 0 0 0.704

113 0 0 0.654 0 0 0.666 0 0 0.704

114 0 0 0.654 0 0 0.666 10 0.02 0.724

115 0 0 0.654 1 0.002 0.668 0 0 0.724

116 0 0 0.654 0 0 0.668 0 0 0.724

117 0 0 0.654 11 0.022 0.69 0 0 0.724

118 0 0 0.654 0 0 0.69 8 0.016 0.74

119 0 0 0.654 10 0.02 0.71 0 0 0.74

120 96 0.192 0.846 0 0 0.71 6 0.012 0.752

121 0 0 0.846 0 0 0.71 0 0 0.752

122 0 0 0.846 0 0 0.71 0 0 0.752

123 0 0 0.846 0 0 0.71 0 0 0.752

124 0 0 0.846 0 0 0.71 3 0.006 0.758

125 0 0 0.846 0 0 0.71 0 0 0.758

126 0 0 0.846 0 0 0.71 0 0 0.758

127 0 0 0.846 0 0 0.71 1 0.002 0.76

128 0 0 0.846 0 0 0.71 0 0 0.76

129 0 0 0.846 0 0 0.71 14 0.028 0.788

130 0 0 0.846 0 0 0.71 0 0 0.788

131 0 0 0.846 0 0 0.71 14 0.028 0.816

132 0 0 0.846 68 0.136 0.846 3 0.006 0.822

133 0 0 0.846 0 0 0.846 0 0 0.822

134 0 0 0.846 0 0 0.846 0 0 0.822

135 0 0 0.846 0 0 0.846 0 0 0.822

136 0 0 0.846 0 0 0.846 0 0 0.822

137 0 0 0.846 0 0 0.846 0 0 0.822

138 0 0 0.846 0 0 0.846 0 0 0.822

139 0 0 0.846 0 0 0.846 0 0 0.822

140 18 0.036 0.882 0 0 0.846 0 0 0.822

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141 0 0 0.882 4 0.008 0.854 1 0.002 0.824

142 0 0 0.882 3 0.006 0.86 4 0.008 0.832

143 0 0 0.882 0 0 0.86 0 0 0.832

144 0 0 0.882 0 0 0.86 22 0.044 0.876

145 0 0 0.882 0 0 0.86 0 0 0.876

146 0 0 0.882 3 0.006 0.866 0 0 0.876

147 0 0 0.882 0 0 0.866 5 0.01 0.886

148 0 0 0.882 0 0 0.866 0 0 0.886

149 0 0 0.882 0 0 0.866 0 0 0.886

150 0 0 0.882 0 0 0.866 0 0 0.886

151 0 0 0.882 0 0 0.866 0 0 0.886

152 0 0 0.882 0 0 0.866 0 0 0.886

153 0 0 0.882 0 0 0.866 0 0 0.886

154 0 0 0.882 14 0.028 0.894 0 0 0.886

155 0 0 0.882 0 0 0.894 4 0.008 0.894

156 0 0 0.882 0 0 0.894 0 0 0.894

157 0 0 0.882 0 0 0.894 0 0 0.894

158 0 0 0.882 0 0 0.894 1 0.002 0.896

159 0 0 0.882 1 0.002 0.896 0 0 0.896

160 42 0.084 0.966 0 0 0.896 0 0 0.896

161 0 0 0.966 5 0.01 0.906 0 0 0.896

162 0 0 0.966 0 0 0.906 9 0.018 0.914

163 0 0 0.966 0 0 0.906 0 0 0.914

164 0 0 0.966 0 0 0.906 0 0 0.914

165 0 0 0.966 0 0 0.906 0 0 0.914

166 0 0 0.966 0 0 0.906 0 0 0.914

167 0 0 0.966 0 0 0.906 0 0 0.914

168 0 0 0.966 0 0 0.906 6 0.012 0.926

169 0 0 0.966 0 0 0.906 0 0 0.926

170 0 0 0.966 0 0 0.906 0 0 0.926

171 0 0 0.966 0 0 0.906 2 0.004 0.93

172 0 0 0.966 0 0 0.906 1 0.002 0.932

173 0 0 0.966 0 0 0.906 0 0 0.932

174 0 0 0.966 0 0 0.906 0 0 0.932

175 0 0 0.966 0 0 0.906 5 0.01 0.942

176 0 0 0.966 30 0.06 0.966 0 0 0.942

177 0 0 0.966 0 0 0.966 4 0.008 0.95

178 0 0 0.966 0 0 0.966 0 0 0.95

179 0 0 0.966 0 0 0.966 0 0 0.95

180 8 0.016 0.982 0 0 0.966 0 0 0.95

181 0 0 0.982 0 0 0.966 0 0 0.95

182 0 0 0.982 0 0 0.966 0 0 0.95

183 0 0 0.982 2 0.004 0.97 0 0 0.95

184 0 0 0.982 0 0 0.97 0 0 0.95

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185 0 0 0.982 0 0 0.97 0 0 0.95

186 0 0 0.982 1 0.002 0.972 1 0.002 0.952

187 0 0 0.982 0 0 0.972 0 0 0.952

188 0 0 0.982 0 0 0.972 0 0 0.952

189 0 0 0.982 0 0 0.972 2 0.004 0.956

190 0 0 0.982 0 0 0.972 0 0 0.956

191 0 0 0.982 0 0 0.972 0 0 0.956

192 0 0 0.982 0 0 0.972 11 0.022 0.978

193 0 0 0.982 0 0 0.972 0 0 0.978

194 0 0 0.982 0 0 0.972 0 0 0.978

195 0 0 0.982 0 0 0.972 0 0 0.978

196 0 0 0.982 0 0 0.972 0 0 0.978

197 0 0 0.982 0 0 0.972 0 0 0.978

198 0 0 0.982 6 0.012 0.984 0 0 0.978

199 0 0 0.982 0 0 0.984 0 0 0.978

200 6 0.012 0.994 0 0 0.984 0 0 0.978

201 0 0 0.994 0 0 0.984 3 0.006 0.984

202 0 0 0.994 0 0 0.984 0 0 0.984

203 0 0 0.994 2 0.004 0.988 0 0 0.984

204 0 0 0.994 0 0 0.988 0 0 0.984

205 0 0 0.994 0 0 0.988 0 0 0.984

206 0 0 0.994 0 0 0.988 0 0 0.984

207 0 0 0.994 0 0 0.988 0 0 0.984

208 0 0 0.994 0 0 0.988 0 0 0.984

209 0 0 0.994 0 0 0.988 0 0 0.984

210 0 0 0.994 0 0 0.988 0 0 0.984

211 0 0 0.994 0 0 0.988 0 0 0.984

212 0 0 0.994 0 0 0.988 0 0 0.984

213 0 0 0.994 0 0 0.988 1 0.002 0.986

214 0 0 0.994 0 0 0.988 0 0 0.986

215 0 0 0.994 0 0 0.988 0 0 0.986

216 0 0 0.994 0 0 0.988 2 0.004 0.99

217 0 0 0.994 0 0 0.988 0 0 0.99

218 0 0 0.994 0 0 0.988 0 0 0.99

219 0 0 0.994 0 0 0.988 0 0 0.99

220 3 0.006 1 3 0.006 0.994 0 0 0.99

221 0 0 1 0 0 0.994 0 0 0.99

222 0 0 1 0 0 0.994 0 0 0.99

223 0 0 1 0 0 0.994 3 0.006 0.996

224 0 0 1 0 0 0.994 0 0 0.996

225 0 0 1 1 0.002 0.996 0 0 0.996

226 0 0 1 0 0 0.996 0 0 0.996

227 0 0 1 0 0 0.996 0 0 0.996

228 0 0 1 0 0 0.996 0 0 0.996

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229 0 0 1 0 0 0.996 0 0 0.996

230 0 0 1 0 0 0.996 1 0.002 0.998

231 0 0 1 0 0 0.996 0 0 0.998

232 0 0 1 0 0 0.996 0 0 0.998

233 0 0 1 0 0 0.996 0 0 0.998

234 0 0 1 0 0 0.996 0 0 0.998

235 0 0 1 0 0 0.996 0 0 0.998

236 0 0 1 0 0 0.996 0 0 0.998

237 0 0 1 0 0 0.996 0 0 0.998

238 0 0 1 0 0 0.996 0 0 0.998

239 0 0 1 0 0 0.996 0 0 0.998

240 0 0 1 0 0 0.996 0 0 0.998

241 0 0 1 0 0 0.996 0 0 0.998

242 0 0 1 2 0.004 1 0 0 0.998

243 0 0 1 0 0 1 0 0 0.998

244 0 0 1 0 0 1 0 0 0.998

245 0 0 1 0 0 1 0 0 0.998

246 0 0 1 0 0 1 0 0 0.998

247 0 0 1 0 0 1 1 0.002 1

248 0 0 1 0 0 1 0 0 1

249 0 0 1 0 0 1 0 0 1

250 0 0 1 0 0 1 0 0 1

Page 26: simulacion_montecarlo2

7 - Beneficios esperados:

BENEFICIO, VARIANZA E INTERVALO GENERADO A PARTIR DE EL Nº DE UNIDADES COMPRADASCANTIDADES 18 19 20 21 22 23 24 25 26BENEFICIO MEDIO 67.46 71.21 74.96 77.86 78.20 75.70 69.78 61.60 52.53DESVIACIÓN TÍPICA 52.81 55.75 58.68 61.41 64.07 66.96 69.34 71.16 72.74INTERVALO CONFIANZA 4.63 4.89 5.14 5.38 5.62 5.87 6.08 6.24 6.38MÁXIMO 72.09 76.10 80.10 83.24 83.82 81.57 75.86 67.84 58.91MÍNIMO 62.83 66.33 69.82 72.48 72.59 69.83 63.71 55.37 46.16

Decisión:

A partir de los beneficios simulados para cada cantidad comprada obtenemos la variable aleatoria beneficios esperados calculando la media de las 1000 simulaciones, y además obtenemos el intervalo de confianza a un nivel del 95 %.

PULSAR F9 PARA RECALCULO ALEATORIO

Los resultados de la simulación indican que la decisión que maximiza el beneficio es realizar un pedido de 22 unidades.

18 19 20 21 22 23 24 25 260.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00BENEFICIO ESPERADO

BENEFICIO MEDIO

MÁXIMO

MÍNIMO

CANTIDADES COMPRADAS SIMULADAS

BE

NE

FIC

IO M

ED

IO E

N 1

000 E

NS

AY

.

Page 27: simulacion_montecarlo2

Los resultados de la simulación indican que la decisión que maximiza el beneficio es realizar un pedido de 22 unidades.


MsnMsgr

MsnMsgr

Paises y puertos

Paises y puertos

Calculo Ciclon

Calculo Ciclon

Formato Financiero-1 (con tabla de amortizacion corregida)

Formato Financiero-1 (con tabla de amortizacion corregida)

3-Sentsoreak

3-Sentsoreak

Report

Report

CLINICA DENTAL PORTUGAL

CLINICA DENTAL PORTUGAL

VALORIZACION OCTUBRE VICTOR ROMERO

VALORIZACION OCTUBRE VICTOR ROMERO

PRECIOSCHACO

PRECIOSCHACO

gidoi teknikoa

gidoi teknikoa

PROFESORADO

PROFESORADO

Albañilería

Albañilería

Kar Español

Kar Español

reinaga - Pensamiento Amautico v2

reinaga - Pensamiento Amautico v2

acrostics

acrostics

BIBLIOGRAFIA

BIBLIOGRAFIA

captura imagen c#

captura imagen c#

Mapas Conceptuales

Mapas Conceptuales

Logos

Logos

CARGUE PUCC

CARGUE PUCC