simulador montecarlo

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

description

plantilla de simulación metodo montecarlo para analisis de riesgos

Transcript of simulador montecarlo

Page 1: simulador montecarlo

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 :

Page 2: simulador montecarlo

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

Page 3: simulador montecarlo

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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Page 4: simulador montecarlo

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 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -32 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 1263 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 294 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -225 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 596 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 657 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -668 24 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 9 15 18 69 24 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 7 233 14 226

10 25 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 9 4111 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 11712 23 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 7 223 14 216 21 20913 24 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 6 114 12 10814 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 015 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 8216 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -5517 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 9118 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 4419 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11120 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -421 21 17 6 7 0 180 0 190 0 200 0 210 7 203 14 196 21 189 28 182 35 17522 22 10 6 7 0 54 0 57 0 60 0 63 0 66 7 59 14 52 21 45 28 3823 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 13024 25 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 0 250 7 24325 24 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 0 216 6 210 12 20426 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -4627 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 1328 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 6529 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 9330 22 10 12 13 0 -54 0 -57 0 -60 0 -63 0 -66 13 -79 26 -92 39 -105 52 -11831 23 17 10 11 0 108 0 114 0 120 0 126 0 132 0 138 11 127 22 116 33 10532 25 17 5 6 0 198 0 209 0 220 0 231 0 242 0 253 0 264 0 275 6 26933 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 7834 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 11735 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -4636 25 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 0 75 7 6837 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 16338 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -5539 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 040 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 10441 21 10 10 11 0 -18 0 -19 0 -20 0 -21 11 -32 22 -43 33 -54 44 -65 55 -7642 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 9143 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 044 24 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 11 37 22 2645 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -446 24 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 7 185 14 17847 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 14848 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -5549 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 2950 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 7451 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 13052 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -2653 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -1354 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -5655 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 9656 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -5257 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -3358 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 10459 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 2960 24 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 9 15 18 661 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 12662 25 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 7 19363 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 7864 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 9365 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 066 22 10 12 13 0 -54 0 -57 0 -60 0 -63 0 -66 13 -79 26 -92 39 -105 52 -11867 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -4468 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 13069 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 6570 21 10 10 11 0 -18 0 -19 0 -20 0 -21 11 -32 22 -43 33 -54 44 -65 55 -7671 20 11 6 7 0 72 0 76 0 80 7 73 14 66 21 59 28 52 35 45 42 3872 25 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 7 19373 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 7174 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11175 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -5576 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 877 22 15 5 6 0 162 0 171 0 180 0 189 0 198 6 192 12 186 18 180 24 17478 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 079 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 1380 22 17 6 7 0 180 0 190 0 200 0 210 0 220 7 213 14 206 21 199 28 192

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81 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 11782 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 3083 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 5284 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 16385 25 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -1386 20 13 10 11 0 36 0 38 0 40 11 29 22 18 33 7 44 -4 55 -15 66 -2687 24 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 0 216 6 210 12 20488 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 9189 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 4890 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -3391 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -5292 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 4493 21 10 10 11 0 -18 0 -19 0 -20 0 -21 11 -32 22 -43 33 -54 44 -65 55 -7694 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 11195 25 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 7 19396 25 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 11 3997 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 6598 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 5299 21 10 12 13 0 -54 0 -57 0 -60 0 -63 13 -76 26 -89 39 -102 52 -115 65 -128

100 20 10 5 6 0 72 0 76 0 80 6 74 12 68 18 62 24 56 30 50 36 44101 23 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 6 109 12 103 18 97102 21 11 5 6 0 90 0 95 0 100 0 105 6 99 12 93 18 87 24 81 30 75103 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163104 22 10 6 7 0 54 0 57 0 60 0 63 0 66 7 59 14 52 21 45 28 38105 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56106 21 11 12 13 0 -36 0 -38 0 -40 0 -42 13 -55 26 -68 39 -81 52 -94 65 -107107 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52108 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8109 22 17 12 13 0 72 0 76 0 80 0 84 0 88 13 75 26 62 39 49 52 36110 20 15 8 9 0 108 0 114 0 120 9 111 18 102 27 93 36 84 45 75 54 66111 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39112 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13113 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52114 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111115 23 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39116 22 17 6 7 0 180 0 190 0 200 0 210 0 220 7 213 14 206 21 199 28 192117 24 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 0 48 13 35 26 22118 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8119 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 59120 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44121 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39122 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52123 23 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 6 201 12 195 18 189124 21 17 12 13 0 72 0 76 0 80 0 84 13 71 26 58 39 45 52 32 65 19125 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89126 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117127 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104128 25 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 9 141129 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 117130 25 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 9 41131 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3132 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163133 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39134 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143135 20 13 10 11 0 36 0 38 0 40 11 29 22 18 33 7 44 -4 55 -15 66 -26136 25 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 6 94137 25 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 7 193138 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 48139 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3140 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89141 22 17 10 11 0 108 0 114 0 120 0 126 0 132 11 121 22 110 33 99 44 88142 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30143 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96144 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3145 23 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 6 109 12 103 18 97146 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 59147 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13148 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89149 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66150 22 11 5 6 0 90 0 95 0 100 0 105 0 110 6 104 12 98 18 92 24 86151 22 10 12 13 0 -54 0 -57 0 -60 0 -63 0 -66 13 -79 26 -92 39 -105 52 -118152 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 91153 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96154 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111155 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 91156 23 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 6 86 12 80 18 74157 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22158 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22159 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71160 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96161 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8162 25 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 9 191163 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163164 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117

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753 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 44754 21 11 6 7 0 72 0 76 0 80 0 84 7 77 14 70 21 63 28 56 35 49755 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30756 25 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13757 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13758 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13759 24 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 7 65 14 58760 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52761 21 13 12 13 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52 65 -65762 25 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 0 125 6 119763 21 15 12 13 0 36 0 38 0 40 0 42 13 29 26 16 39 3 52 -10 65 -23764 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3765 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130766 20 17 10 11 0 108 0 114 0 120 11 109 22 98 33 87 44 76 55 65 66 54767 25 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 9 141768 21 10 5 6 0 72 0 76 0 80 0 84 6 78 12 72 18 66 24 60 30 54769 20 13 5 6 0 126 0 133 0 140 6 134 12 128 18 122 24 116 30 110 36 104770 20 13 8 9 0 72 0 76 0 80 9 71 18 62 27 53 36 44 45 35 54 26771 21 10 12 13 0 -54 0 -57 0 -60 0 -63 13 -76 26 -89 39 -102 52 -115 65 -128772 23 17 10 11 0 108 0 114 0 120 0 126 0 132 0 138 11 127 22 116 33 105773 22 17 10 11 0 108 0 114 0 120 0 126 0 132 11 121 22 110 33 99 44 88774 24 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 7 233 14 226775 22 17 6 7 0 180 0 190 0 200 0 210 0 220 7 213 14 206 21 199 28 192776 21 11 5 6 0 90 0 95 0 100 0 105 6 99 12 93 18 87 24 81 30 75777 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65778 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29779 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55780 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 82781 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65782 22 17 5 6 0 198 0 209 0 220 0 231 0 242 6 236 12 230 18 224 24 218783 21 10 5 6 0 72 0 76 0 80 0 84 6 78 12 72 18 66 24 60 30 54784 20 13 8 9 0 72 0 76 0 80 9 71 18 62 27 53 36 44 45 35 54 26785 23 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 9 175 18 166 27 157786 20 15 10 11 0 72 0 76 0 80 11 69 22 58 33 47 44 36 55 25 66 14787 20 13 6 7 0 108 0 114 0 120 7 113 14 106 21 99 28 92 35 85 42 78788 22 17 8 9 0 144 0 152 0 160 0 168 0 176 9 167 18 158 27 149 36 140789 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -46790 21 11 5 6 0 90 0 95 0 100 0 105 6 99 12 93 18 87 24 81 30 75791 24 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 11 37 22 26792 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65793 25 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 0 168 0 175 6 169794 25 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 13 37795 23 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 7 223 14 216 21 209796 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78797 25 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 9 141798 20 10 5 6 0 72 0 76 0 80 6 74 12 68 18 62 24 56 30 50 36 44799 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8800 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 82801 25 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 9 141802 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81803 20 11 10 11 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55 66 -66804 20 17 8 9 0 144 0 152 0 160 9 151 18 142 27 133 36 124 45 115 54 106805 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19806 21 15 12 13 0 36 0 38 0 40 0 42 13 29 26 16 39 3 52 -10 65 -23807 20 11 10 11 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55 66 -66808 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65809 22 11 5 6 0 90 0 95 0 100 0 105 0 110 6 104 12 98 18 92 24 86810 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 74811 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89812 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19813 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44814 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30815 22 15 10 11 0 72 0 76 0 80 0 84 0 88 11 77 22 66 33 55 44 44816 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117817 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65818 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52819 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 117820 21 17 12 13 0 72 0 76 0 80 0 84 13 71 26 58 39 45 52 32 65 19821 24 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22822 21 11 6 7 0 72 0 76 0 80 0 84 7 77 14 70 21 63 28 56 35 49823 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39824 21 11 6 7 0 72 0 76 0 80 0 84 7 77 14 70 21 63 28 56 35 49825 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -46826 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65827 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26828 24 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 0 96 6 90 12 84829 20 11 8 9 0 36 0 38 0 40 9 31 18 22 27 13 36 4 45 -5 54 -14830 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130831 25 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 13 37832 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 93833 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163834 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8835 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130836 25 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 9 91

Page 15: simulador montecarlo

837 23 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39838 20 11 6 7 0 72 0 76 0 80 7 73 14 66 21 59 28 52 35 45 42 38839 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78840 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8841 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 133842 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163843 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0844 23 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 11 -34 22 -45 33 -56845 24 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 0 24 9 15 18 6846 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14847 21 10 6 7 0 54 0 57 0 60 0 63 7 56 14 49 21 42 28 35 35 28848 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 126849 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104850 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0851 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111852 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52853 25 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 9 41854 24 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 11 37 22 26855 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66856 24 17 8 9 0 144 0 152 0 160 0 168 0 176 0 184 0 192 9 183 18 174857 22 11 5 6 0 90 0 95 0 100 0 105 0 110 6 104 12 98 18 92 24 86858 23 10 8 9 0 18 0 19 0 20 0 21 0 22 0 23 9 14 18 5 27 -4859 20 15 5 6 0 162 0 171 0 180 6 174 12 168 18 162 24 156 30 150 36 144860 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39861 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96862 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78863 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26864 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 126865 21 15 12 13 0 36 0 38 0 40 0 42 13 29 26 16 39 3 52 -10 65 -23866 20 15 8 9 0 108 0 114 0 120 9 111 18 102 27 93 36 84 45 75 54 66867 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 126868 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52869 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130870 25 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 0 250 7 243871 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39872 24 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 11 -35 22 -46873 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163874 25 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 0 150 7 143875 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65876 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0877 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163878 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65879 24 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 0 240 7 233 14 226880 25 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 7 193881 22 11 6 7 0 72 0 76 0 80 0 84 0 88 7 81 14 74 21 67 28 60882 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8883 22 11 6 7 0 72 0 76 0 80 0 84 0 88 7 81 14 74 21 67 28 60884 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14885 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3886 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71887 23 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 11 35 22 24 33 13888 23 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 11 81 22 70 33 59889 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8890 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104891 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52892 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -24893 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33894 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 133895 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66896 22 10 12 13 0 -54 0 -57 0 -60 0 -63 0 -66 13 -79 26 -92 39 -105 52 -118897 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52898 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65899 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52900 24 11 5 6 0 90 0 95 0 100 0 105 0 110 0 115 0 120 6 114 12 108901 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71902 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39903 25 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 0 -25 11 -36904 23 17 6 7 0 180 0 190 0 200 0 210 0 220 0 230 7 223 14 216 21 209905 25 11 12 13 0 -36 0 -38 0 -40 0 -42 0 -44 0 -46 0 -48 0 -50 13 -63906 24 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 0 96 9 87 18 78907 21 10 5 6 0 72 0 76 0 80 0 84 6 78 12 72 18 66 24 60 30 54908 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111909 23 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 7 177 14 170 21 163910 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30911 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96912 22 11 8 9 0 36 0 38 0 40 0 42 0 44 9 35 18 26 27 17 36 8913 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89914 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 48915 23 13 5 6 0 126 0 133 0 140 0 147 0 154 0 161 6 155 12 149 18 143916 22 13 8 9 0 72 0 76 0 80 0 84 0 88 9 79 18 70 27 61 36 52917 24 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 0 48 9 39 18 30918 23 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33919 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55920 24 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 11 85 22 74

Page 16: simulador montecarlo

921 22 11 6 7 0 72 0 76 0 80 0 84 0 88 7 81 14 74 21 67 28 60922 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14923 22 17 5 6 0 198 0 209 0 220 0 231 0 242 6 236 12 230 18 224 24 218924 25 10 5 6 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 6 94925 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39926 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55927 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65928 25 13 10 11 0 36 0 38 0 40 0 42 0 44 0 46 0 48 0 50 11 39929 22 10 8 9 0 18 0 19 0 20 0 21 0 22 9 13 18 4 27 -5 36 -14930 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148931 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 93932 24 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 0 144 9 135 18 126933 20 15 6 7 0 144 0 152 0 160 7 153 14 146 21 139 28 132 35 125 42 118934 24 17 5 6 0 198 0 209 0 220 0 231 0 242 0 253 0 264 6 258 12 252935 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148936 21 13 5 6 0 126 0 133 0 140 0 147 6 141 12 135 18 129 24 123 30 117937 25 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 0 -23 0 -24 0 -25 11 -36938 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0939 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3940 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104941 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26942 25 11 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 -11943 22 15 6 7 0 144 0 152 0 160 0 168 0 176 7 169 14 162 21 155 28 148944 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 91945 23 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 7 62 14 55 21 48946 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117947 20 17 10 11 0 108 0 114 0 120 11 109 22 98 33 87 44 76 55 65 66 54948 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -24949 24 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 7 65 14 58950 23 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 7 85 14 78 21 71951 22 17 8 9 0 144 0 152 0 160 0 168 0 176 9 167 18 158 27 149 36 140952 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130953 20 13 8 9 0 72 0 76 0 80 9 71 18 62 27 53 36 44 45 35 54 26954 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13955 22 13 12 13 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52956 25 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 0 75 7 68957 21 13 8 9 0 72 0 76 0 80 0 84 9 75 18 66 27 57 36 48 45 39958 25 15 6 7 0 144 0 152 0 160 0 168 0 176 0 184 0 192 0 200 7 193959 23 15 12 13 0 36 0 38 0 40 0 42 0 44 0 46 13 33 26 20 39 7960 23 15 5 6 0 162 0 171 0 180 0 189 0 198 0 207 6 201 12 195 18 189961 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13962 20 17 5 6 0 198 0 209 0 220 6 214 12 208 18 202 24 196 30 190 36 184963 23 11 8 9 0 36 0 38 0 40 0 42 0 44 0 46 9 37 18 28 27 19964 21 10 8 9 0 18 0 19 0 20 0 21 9 12 18 3 27 -6 36 -15 45 -24965 24 13 12 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 -13 26 -26966 20 15 5 6 0 162 0 171 0 180 6 174 12 168 18 162 24 156 30 150 36 144967 23 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 7 131 14 124 21 117968 22 13 10 11 0 36 0 38 0 40 0 42 0 44 11 33 22 22 33 11 44 0969 21 15 10 11 0 72 0 76 0 80 0 84 11 73 22 62 33 51 44 40 55 29970 21 13 6 7 0 108 0 114 0 120 0 126 7 119 14 112 21 105 28 98 35 91971 22 10 10 11 0 -18 0 -19 0 -20 0 -21 0 -22 11 -33 22 -44 33 -55 44 -66972 23 15 8 9 0 108 0 114 0 120 0 126 0 132 0 138 9 129 18 120 27 111973 25 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 7 93974 22 13 5 6 0 126 0 133 0 140 0 147 0 154 6 148 12 142 18 136 24 130975 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13976 24 11 6 7 0 72 0 76 0 80 0 84 0 88 0 92 0 96 7 89 14 82977 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3978 24 10 6 7 0 54 0 57 0 60 0 63 0 66 0 69 0 72 7 65 14 58979 21 11 8 9 0 36 0 38 0 40 0 42 9 33 18 24 27 15 36 6 45 -3980 25 15 10 11 0 72 0 76 0 80 0 84 0 88 0 92 0 96 0 100 11 89981 20 11 8 9 0 36 0 38 0 40 9 31 18 22 27 13 36 4 45 -5 54 -14982 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44983 21 17 10 11 0 108 0 114 0 120 0 126 11 115 22 104 33 93 44 82 55 71984 20 10 8 9 0 18 0 19 0 20 9 11 18 2 27 -7 36 -16 45 -25 54 -34985 22 11 10 11 0 0 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44986 21 11 10 11 0 0 0 0 0 0 0 0 11 -11 22 -22 33 -33 44 -44 55 -55987 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130988 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13989 23 17 12 13 0 72 0 76 0 80 0 84 0 88 0 92 13 79 26 66 39 53990 21 11 12 13 0 -36 0 -38 0 -40 0 -42 13 -55 26 -68 39 -81 52 -94 65 -107991 21 13 12 13 0 0 0 0 0 0 0 0 13 -13 26 -26 39 -39 52 -52 65 -65992 22 13 6 7 0 108 0 114 0 120 0 126 0 132 7 125 14 118 21 111 28 104993 21 15 6 7 0 144 0 152 0 160 0 168 7 161 14 154 21 147 28 140 35 133994 22 15 8 9 0 108 0 114 0 120 0 126 0 132 9 123 18 114 27 105 36 96995 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130996 24 13 6 7 0 108 0 114 0 120 0 126 0 132 0 138 0 144 7 137 14 130997 21 13 10 11 0 36 0 38 0 40 0 42 11 31 22 20 33 9 44 -2 55 -13998 21 17 10 11 0 108 0 114 0 120 0 126 11 115 22 104 33 93 44 82 55 71999 23 13 8 9 0 72 0 76 0 80 0 84 0 88 0 92 9 83 18 74 27 65

1000 21 15 8 9 0 108 0 114 0 120 0 126 9 117 18 108 27 99 36 90 45 81

Page 17: simulador montecarlo

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 1 0.002 0.004

-101 0 0 0 0 0 0 0 0 0.004

-100 0 0 0 0 0 0 0 0 0.004

-99 0 0 0 0 0 0 0 0 0.004

-98 0 0 0 0 0 0 0 0 0.004

-97 0 0 0 0 0 0 0 0 0.004

-96 0 0 0 0 0 0 0 0 0.004

-95 0 0 0 0 0 0 0 0 0.004

-94 0 0 0 0 0 0 0 0 0.004

-93 0 0 0 0 0 0 0 0 0.004

-92 0 0 0 0 0 0 6 0.012 0.016

-91 0 0 0 0 0 0 0 0 0.016

-90 0 0 0 0 0 0 0 0 0.016

-89 0 0 0 0 0 0 0 0 0.016

-88 0 0 0 0 0 0 0 0 0.016

-87 0 0 0 0 0 0 0 0 0.016

-86 0 0 0 1 0.002 0.002 0 0 0.016

-85 0 0 0 0 0 0.002 0 0 0.016

-84 0 0 0 0 0 0.002 0 0 0.016

-83 0 0 0 0 0 0.002 0 0 0.016

-82 0 0 0 0 0 0.002 0 0 0.016

-81 0 0 0 0 0 0.002 2 0.004 0.02

-80 0 0 0 0 0 0.002 0 0 0.02

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: simulador montecarlo

-79 0 0 0 0 0 0.002 0 0 0.02

-78 0 0 0 0 0 0.002 0 0 0.02

-77 0 0 0 0 0 0.002 0 0 0.02

-76 0 0 0 1 0.002 0.004 0 0 0.02

-75 0 0 0 0 0 0.004 0 0 0.02

-74 0 0 0 0 0 0.004 0 0 0.02

-73 0 0 0 0 0 0.004 0 0 0.02

-72 0 0 0 0 0 0.004 3 0.006 0.026

-71 0 0 0 0 0 0.004 0 0 0.026

-70 0 0 0 0 0 0.004 2 0.004 0.03

-69 0 0 0 0 0 0.004 0 0 0.03

-68 0 0 0 0 0 0.004 0 0 0.03

-67 0 0 0 0 0 0.004 0 0 0.03

-66 0 0 0 9 0.018 0.022 0 0 0.03

-65 0 0 0 0 0 0.022 0 0 0.03

-64 0 0 0 0 0 0.022 2 0.004 0.034

-63 0 0 0 0 0 0.022 0 0 0.034

-62 0 0 0 0 0 0.022 0 0 0.034

-61 0 0 0 0 0 0.022 0 0 0.034

-60 10 0.02 0.02 0 0 0.022 0 0 0.034

-59 0 0 0.02 0 0 0.022 1 0.002 0.036

-58 0 0 0.02 0 0 0.022 0 0 0.036

-57 0 0 0.02 0 0 0.022 0 0 0.036

-56 0 0 0.02 0 0 0.022 0 0 0.036

-55 0 0 0.02 2 0.004 0.026 0 0 0.036

-54 0 0 0.02 0 0 0.026 5 0.01 0.046

-53 0 0 0.02 0 0 0.026 0 0 0.046

-52 0 0 0.02 0 0 0.026 1 0.002 0.048

-51 0 0 0.02 0 0 0.026 0 0 0.048

-50 0 0 0.02 0 0 0.026 0 0 0.048

-49 0 0 0.02 0 0 0.026 0 0 0.048

-48 0 0 0.02 0 0 0.026 2 0.004 0.052

-47 0 0 0.02 0 0 0.026 0 0 0.052

-46 0 0 0.02 0 0 0.026 0 0 0.052

-45 0 0 0.02 0 0 0.026 0 0 0.052

-44 0 0 0.02 5 0.01 0.036 8 0.016 0.068

-43 0 0 0.02 0 0 0.036 0 0 0.068

-42 0 0 0.02 2 0.004 0.04 0 0 0.068

-41 0 0 0.02 0 0 0.04 0 0 0.068

-40 8 0.016 0.036 0 0 0.04 0 0 0.068

-39 0 0 0.036 0 0 0.04 2 0.004 0.072

-38 0 0 0.036 0 0 0.04 0 0 0.072

-37 0 0 0.036 0 0 0.04 0 0 0.072

-36 0 0 0.036 0 0 0.04 0 0 0.072

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-35 0 0 0.036 0 0 0.04 0 0 0.072

-34 0 0 0.036 0 0 0.04 6 0.012 0.084

-33 0 0 0.036 0 0 0.04 9 0.018 0.102

-32 0 0 0.036 5 0.01 0.05 0 0 0.102

-31 0 0 0.036 0 0 0.05 0 0 0.102

-30 0 0 0.036 0 0 0.05 0 0 0.102

-29 0 0 0.036 0 0 0.05 0 0 0.102

-28 0 0 0.036 0 0 0.05 0 0 0.102

-27 0 0 0.036 0 0 0.05 0 0 0.102

-26 0 0 0.036 1 0.002 0.052 6 0.012 0.114

-25 0 0 0.036 0 0 0.052 0 0 0.114

-24 0 0 0.036 0 0 0.052 3 0.006 0.12

-23 0 0 0.036 0 0 0.052 0 0 0.12

-22 0 0 0.036 17 0.034 0.086 5 0.01 0.13

-21 0 0 0.036 0 0 0.086 0 0 0.13

-20 23 0.046 0.082 0 0 0.086 0 0 0.13

-19 0 0 0.082 0 0 0.086 0 0 0.13

-18 0 0 0.082 0 0 0.086 0 0 0.13

-17 0 0 0.082 0 0 0.086 0 0 0.13

-16 0 0 0.082 0 0 0.086 0 0 0.13

-15 0 0 0.082 0 0 0.086 0 0 0.13

-14 0 0 0.082 0 0 0.086 0 0 0.13

-13 0 0 0.082 2 0.004 0.09 3 0.006 0.136

-12 0 0 0.082 0 0 0.09 2 0.004 0.14

-11 0 0 0.082 9 0.018 0.108 3 0.006 0.146

-10 0 0 0.082 0 0 0.108 0 0 0.146

-9 0 0 0.082 0 0 0.108 0 0 0.146

-8 0 0 0.082 0 0 0.108 0 0 0.146

-7 0 0 0.082 0 0 0.108 0 0 0.146

-6 0 0 0.082 0 0 0.108 2 0.004 0.15

-5 0 0 0.082 0 0 0.108 0 0 0.15

-4 0 0 0.082 0 0 0.108 2 0.004 0.154

-3 0 0 0.082 0 0 0.108 0 0 0.154

-2 0 0 0.082 0 0 0.108 0 0 0.154

-1 0 0 0.082 0 0 0.108 0 0 0.154

0 47 0.094 0.176 34 0.068 0.176 17 0.034 0.188

1 0 0 0.176 0 0 0.176 0 0 0.188

2 0 0 0.176 0 0 0.176 0 0 0.188

3 0 0 0.176 0 0 0.176 1 0.002 0.19

4 0 0 0.176 0 0 0.176 8 0.016 0.206

5 0 0 0.176 0 0 0.176 0 0 0.206

6 0 0 0.176 0 0 0.176 0 0 0.206

7 0 0 0.176 0 0 0.176 0 0 0.206

8 0 0 0.176 0 0 0.176 0 0 0.206

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9 0 0 0.176 0 0 0.176 6 0.012 0.218

10 0 0 0.176 0 0 0.176 0 0 0.218

11 0 0 0.176 0 0 0.176 0 0 0.218

12 0 0 0.176 2 0.004 0.18 0 0 0.218

13 0 0 0.176 0 0 0.18 0 0 0.218

14 0 0 0.176 2 0.004 0.184 7 0.014 0.232

15 0 0 0.176 0 0 0.184 10 0.02 0.252

16 0 0 0.176 0 0 0.184 0 0 0.252

17 0 0 0.176 0 0 0.184 0 0 0.252

18 0 0 0.176 2 0.004 0.188 0 0 0.252

19 0 0 0.176 0 0 0.188 0 0 0.252

20 19 0.038 0.214 0 0 0.188 0 0 0.252

21 0 0 0.214 0 0 0.188 0 0 0.252

22 0 0 0.214 21 0.042 0.23 16 0.032 0.284

23 0 0 0.214 0 0 0.23 0 0 0.284

24 0 0 0.214 0 0 0.23 6 0.012 0.296

25 0 0 0.214 0 0 0.23 0 0 0.296

26 0 0 0.214 0 0 0.23 9 0.018 0.314

27 0 0 0.214 0 0 0.23 0 0 0.314

28 0 0 0.214 0 0 0.23 0 0 0.314

29 0 0 0.214 1 0.002 0.232 0 0 0.314

30 0 0 0.214 0 0 0.232 0 0 0.314

31 0 0 0.214 6 0.012 0.244 0 0 0.314

32 0 0 0.214 0 0 0.244 1 0.002 0.316

33 0 0 0.214 10 0.02 0.264 2 0.004 0.32

34 0 0 0.214 0 0 0.264 0 0 0.32

35 0 0 0.214 0 0 0.264 8 0.016 0.336

36 0 0 0.214 0 0 0.264 3 0.006 0.342

37 0 0 0.214 0 0 0.264 9 0.018 0.36

38 0 0 0.214 0 0 0.264 0 0 0.36

39 0 0 0.214 0 0 0.264 0 0 0.36

40 86 0.172 0.386 0 0 0.264 0 0 0.36

41 0 0 0.386 0 0 0.264 0 0 0.36

42 0 0 0.386 0 0 0.264 2 0.004 0.364

43 0 0 0.386 0 0 0.264 0 0 0.364

44 0 0 0.386 61 0.122 0.386 1 0.002 0.366

45 0 0 0.386 0 0 0.386 1 0.002 0.368

46 0 0 0.386 1 0.002 0.388 0 0 0.368

47 0 0 0.386 0 0 0.388 0 0 0.368

48 0 0 0.386 0 0 0.388 17 0.034 0.402

49 0 0 0.386 0 0 0.388 0 0 0.402

50 0 0 0.386 0 0 0.388 0 0 0.402

51 0 0 0.386 0 0 0.388 6 0.012 0.414

52 0 0 0.386 0 0 0.388 10 0.02 0.434

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53 0 0 0.386 0 0 0.388 0 0 0.434

54 0 0 0.386 0 0 0.388 0 0 0.434

55 0 0 0.386 0 0 0.388 0 0 0.434

56 0 0 0.386 2 0.004 0.392 1 0.002 0.436

57 0 0 0.386 0 0 0.392 12 0.024 0.46

58 0 0 0.386 3 0.006 0.398 0 0 0.46

59 0 0 0.386 0 0 0.398 0 0 0.46

60 18 0.036 0.422 0 0 0.398 0 0 0.46

61 0 0 0.422 0 0 0.398 0 0 0.46

62 0 0 0.422 1 0.002 0.4 7 0.014 0.474

63 0 0 0.422 0 0 0.4 2 0.004 0.478

64 0 0 0.422 0 0 0.4 0 0 0.478

65 0 0 0.422 0 0 0.4 0 0 0.478

66 0 0 0.422 19 0.038 0.438 9 0.018 0.496

67 0 0 0.422 0 0 0.438 0 0 0.496

68 0 0 0.422 1 0.002 0.44 0 0 0.496

69 0 0 0.422 0 0 0.44 0 0 0.496

70 0 0 0.422 0 0 0.44 14 0.028 0.524

71 0 0 0.422 1 0.002 0.442 0 0 0.524

72 0 0 0.422 0 0 0.442 4 0.008 0.532

73 0 0 0.422 6 0.012 0.454 0 0 0.532

74 0 0 0.422 0 0 0.454 5 0.01 0.542

75 0 0 0.422 12 0.024 0.478 0 0 0.542

76 0 0 0.422 0 0 0.478 3 0.006 0.548

77 0 0 0.422 2 0.004 0.482 0 0 0.548

78 0 0 0.422 0 0 0.482 0 0 0.548

79 0 0 0.422 0 0 0.482 3 0.006 0.554

80 124 0.248 0.67 0 0 0.482 0 0 0.554

81 0 0 0.67 0 0 0.482 8 0.016 0.57

82 0 0 0.67 0 0 0.482 0 0 0.57

83 0 0 0.67 0 0 0.482 14 0.028 0.598

84 0 0 0.67 0 0 0.482 3 0.006 0.604

85 0 0 0.67 0 0 0.482 3 0.006 0.61

86 0 0 0.67 0 0 0.482 4 0.008 0.618

87 0 0 0.67 0 0 0.482 5 0.01 0.628

88 0 0 0.67 95 0.19 0.672 0 0 0.628

89 0 0 0.67 0 0 0.672 0 0 0.628

90 0 0 0.67 0 0 0.672 0 0 0.628

91 0 0 0.67 0 0 0.672 0 0 0.628

92 0 0 0.67 0 0 0.672 4 0.008 0.636

93 0 0 0.67 0 0 0.672 1 0.002 0.638

94 0 0 0.67 0 0 0.672 0 0 0.638

95 0 0 0.67 0 0 0.672 0 0 0.638

96 0 0 0.67 0 0 0.672 31 0.062 0.7

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97 0 0 0.67 0 0 0.672 0 0 0.7

98 0 0 0.67 1 0.002 0.674 3 0.006 0.706

99 0 0 0.67 5 0.01 0.684 3 0.006 0.712

100 18 0.036 0.706 0 0 0.684 0 0 0.712

101 0 0 0.706 0 0 0.684 0 0 0.712

102 0 0 0.706 3 0.006 0.69 0 0 0.712

103 0 0 0.706 0 0 0.69 0 0 0.712

104 0 0 0.706 0 0 0.69 0 0 0.712

105 0 0 0.706 0 0 0.69 4 0.008 0.72

106 0 0 0.706 4 0.008 0.698 0 0 0.72

107 0 0 0.706 0 0 0.698 0 0 0.72

108 0 0 0.706 0 0 0.698 0 0 0.72

109 0 0 0.706 0 0 0.698 6 0.012 0.732

110 0 0 0.706 12 0.024 0.722 1 0.002 0.734

111 0 0 0.706 0 0 0.722 0 0 0.734

112 0 0 0.706 0 0 0.722 0 0 0.734

113 0 0 0.706 0 0 0.722 0 0 0.734

114 0 0 0.706 0 0 0.722 9 0.018 0.752

115 0 0 0.706 1 0.002 0.724 0 0 0.752

116 0 0 0.706 0 0 0.724 1 0.002 0.754

117 0 0 0.706 3 0.006 0.73 0 0 0.754

118 0 0 0.706 0 0 0.73 8 0.016 0.77

119 0 0 0.706 4 0.008 0.738 0 0 0.77

120 63 0.126 0.832 0 0 0.738 3 0.006 0.776

121 0 0 0.832 0 0 0.738 0 0 0.776

122 0 0 0.832 0 0 0.738 0 0 0.776

123 0 0 0.832 0 0 0.738 0 0 0.776

124 0 0 0.832 0 0 0.738 1 0.002 0.778

125 0 0 0.832 0 0 0.738 0 0 0.778

126 0 0 0.832 0 0 0.738 0 0 0.778

127 0 0 0.832 0 0 0.738 2 0.004 0.782

128 0 0 0.832 1 0.002 0.74 0 0 0.782

129 0 0 0.832 0 0 0.74 11 0.022 0.804

130 0 0 0.832 0 0 0.74 0 0 0.804

131 0 0 0.832 0 0 0.74 8 0.016 0.82

132 0 0 0.832 47 0.094 0.834 1 0.002 0.822

133 0 0 0.832 0 0 0.834 0 0 0.822

134 0 0 0.832 0 0 0.834 0 0 0.822

135 0 0 0.832 0 0 0.834 0 0 0.822

136 0 0 0.832 0 0 0.834 0 0 0.822

137 0 0 0.832 0 0 0.834 0 0 0.822

138 0 0 0.832 0 0 0.834 0 0 0.822

139 0 0 0.832 0 0 0.834 0 0 0.822

140 18 0.036 0.868 0 0 0.834 0 0 0.822

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141 0 0 0.868 4 0.008 0.842 1 0.002 0.824

142 0 0 0.868 1 0.002 0.844 6 0.012 0.836

143 0 0 0.868 0 0 0.844 0 0 0.836

144 0 0 0.868 0 0 0.844 12 0.024 0.86

145 0 0 0.868 0 0 0.844 0 0 0.86

146 0 0 0.868 1 0.002 0.846 0 0 0.86

147 0 0 0.868 0 0 0.846 2 0.004 0.864

148 0 0 0.868 0 0 0.846 0 0 0.864

149 0 0 0.868 0 0 0.846 0 0 0.864

150 0 0 0.868 0 0 0.846 0 0 0.864

151 0 0 0.868 0 0 0.846 0 0 0.864

152 0 0 0.868 0 0 0.846 0 0 0.864

153 0 0 0.868 0 0 0.846 0 0 0.864

154 0 0 0.868 13 0.026 0.872 0 0 0.864

155 0 0 0.868 0 0 0.872 3 0.006 0.87

156 0 0 0.868 0 0 0.872 1 0.002 0.872

157 0 0 0.868 0 0 0.872 0 0 0.872

158 0 0 0.868 0 0 0.872 2 0.004 0.876

159 0 0 0.868 1 0.002 0.874 0 0 0.876

160 35 0.07 0.938 0 0 0.874 0 0 0.876

161 0 0 0.938 2 0.004 0.878 0 0 0.876

162 0 0 0.938 0 0 0.878 5 0.01 0.886

163 0 0 0.938 0 0 0.878 0 0 0.886

164 0 0 0.938 0 0 0.878 0 0 0.886

165 0 0 0.938 0 0 0.878 0 0 0.886

166 0 0 0.938 0 0 0.878 0 0 0.886

167 0 0 0.938 0 0 0.878 0 0 0.886

168 0 0 0.938 1 0.002 0.88 4 0.008 0.894

169 0 0 0.938 0 0 0.88 0 0 0.894

170 0 0 0.938 0 0 0.88 0 0 0.894

171 0 0 0.938 0 0 0.88 3 0.006 0.9

172 0 0 0.938 0 0 0.88 0 0 0.9

173 0 0 0.938 0 0 0.88 0 0 0.9

174 0 0 0.938 0 0 0.88 0 0 0.9

175 0 0 0.938 0 0 0.88 2 0.004 0.904

176 0 0 0.938 30 0.06 0.94 0 0 0.904

177 0 0 0.938 0 0 0.94 11 0.022 0.926

178 0 0 0.938 0 0 0.94 0 0 0.926

179 0 0 0.938 0 0 0.94 0 0 0.926

180 15 0.03 0.968 0 0 0.94 0 0 0.926

181 0 0 0.968 0 0 0.94 0 0 0.926

182 0 0 0.968 0 0 0.94 0 0 0.926

183 0 0 0.968 3 0.006 0.946 0 0 0.926

184 0 0 0.968 0 0 0.946 0 0 0.926

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185 0 0 0.968 0 0 0.946 0 0 0.926

186 0 0 0.968 0 0 0.946 5 0.01 0.936

187 0 0 0.968 0 0 0.946 0 0 0.936

188 0 0 0.968 0 0 0.946 0 0 0.936

189 0 0 0.968 0 0 0.946 1 0.002 0.938

190 0 0 0.968 0 0 0.946 0 0 0.938

191 0 0 0.968 0 0 0.946 0 0 0.938

192 0 0 0.968 0 0 0.946 10 0.02 0.958

193 0 0 0.968 0 0 0.946 0 0 0.958

194 0 0 0.968 0 0 0.946 0 0 0.958

195 0 0 0.968 0 0 0.946 0 0 0.958

196 0 0 0.968 0 0 0.946 0 0 0.958

197 0 0 0.968 0 0 0.946 0 0 0.958

198 0 0 0.968 11 0.022 0.968 0 0 0.958

199 0 0 0.968 0 0 0.968 0 0 0.958

200 9 0.018 0.986 0 0 0.968 0 0 0.958

201 0 0 0.986 0 0 0.968 4 0.008 0.966

202 0 0 0.986 0 0 0.968 0 0 0.966

203 0 0 0.986 1 0.002 0.97 0 0 0.966

204 0 0 0.986 0 0 0.97 0 0 0.966

205 0 0 0.986 0 0 0.97 0 0 0.966

206 0 0 0.986 0 0 0.97 4 0.008 0.974

207 0 0 0.986 0 0 0.97 0 0 0.974

208 0 0 0.986 0 0 0.97 0 0 0.974

209 0 0 0.986 0 0 0.97 0 0 0.974

210 0 0 0.986 0 0 0.97 0 0 0.974

211 0 0 0.986 0 0 0.97 0 0 0.974

212 0 0 0.986 0 0 0.97 0 0 0.974

213 0 0 0.986 0 0 0.97 0 0 0.974

214 0 0 0.986 0 0 0.97 0 0 0.974

215 0 0 0.986 0 0 0.97 0 0 0.974

216 0 0 0.986 0 0 0.97 2 0.004 0.978

217 0 0 0.986 0 0 0.97 0 0 0.978

218 0 0 0.986 0 0 0.97 0 0 0.978

219 0 0 0.986 0 0 0.97 0 0 0.978

220 7 0.014 1 8 0.016 0.986 0 0 0.978

221 0 0 1 0 0 0.986 0 0 0.978

222 0 0 1 0 0 0.986 0 0 0.978

223 0 0 1 0 0 0.986 1 0.002 0.98

224 0 0 1 0 0 0.986 0 0 0.98

225 0 0 1 0 0 0.986 0 0 0.98

226 0 0 1 0 0 0.986 0 0 0.98

227 0 0 1 0 0 0.986 0 0 0.98

228 0 0 1 0 0 0.986 0 0 0.98

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229 0 0 1 0 0 0.986 0 0 0.98

230 0 0 1 0 0 0.986 2 0.004 0.984

231 0 0 1 0 0 0.986 0 0 0.984

232 0 0 1 0 0 0.986 0 0 0.984

233 0 0 1 0 0 0.986 0 0 0.984

234 0 0 1 0 0 0.986 0 0 0.984

235 0 0 1 0 0 0.986 0 0 0.984

236 0 0 1 0 0 0.986 0 0 0.984

237 0 0 1 0 0 0.986 0 0 0.984

238 0 0 1 0 0 0.986 0 0 0.984

239 0 0 1 0 0 0.986 0 0 0.984

240 0 0 1 0 0 0.986 3 0.006 0.99

241 0 0 1 0 0 0.986 0 0 0.99

242 0 0 1 7 0.014 1 0 0 0.99

243 0 0 1 0 0 1 0 0 0.99

244 0 0 1 0 0 1 0 0 0.99

245 0 0 1 0 0 1 0 0 0.99

246 0 0 1 0 0 1 0 0 0.99

247 0 0 1 0 0 1 0 0 0.99

248 0 0 1 0 0 1 0 0 0.99

249 0 0 1 0 0 1 0 0 0.99

250 0 0 1 0 0 1 0 0 0.99

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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 66.53 70.22 73.92 76.67 77.29 74.41 68.44 60.49 51.41DESVIACIÓN TÍPICA 54.75 57.79 60.83 63.91 67.36 70.70 73.44 75.70 77.32INTERVALO CONFIANZA 4.80 5.07 5.33 5.60 5.90 6.20 6.44 6.64 6.78MÁXIMO 71.33 75.29 79.25 82.27 83.20 80.61 74.88 67.13 58.18MÍNIMO 61.73 65.16 68.59 71.07 71.39 68.22 62.00 53.86 44.63

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

.

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