1. Define simulation.

2. What are the advantages and limitation of simulation?

1. At a service station, a study was made over a period of 25 days to determine both the number of automobiles being brought in service and the number of automobiles serviced. The results are given below:

No. of automobiles arriving for service or completing service per day | Frequency of arrivals for service | Frequency of daily completion |
---|---|---|

0 | 2 | 3 |

1 | 4 | 2 |

2 | 10 | 12 |

3 | 5 | 3 |

4 | 3 | 4 |

5 | 1 | 1 |

Simulate the arrival pattern for a ten day period and estimate the mean number of automobiles that remain in service for more than one day.

2. The Lajwaab Bakery House keeps stock of a popular brand of cake. Daily demand based on past experience indicates

Daily Demand | : | 0 | 15 | 25 | 35 | 45 | 50 |

Probability | : | .01 | .15 | .20 | .50 | .12 | .02 |

Consider the following sequence of random numbers:-

R. No. 48, 68, 09, 51, 56, 70, 15, 34, 68, 19, 22, 90, 30, 41, 50

Using this sequence, simulate the demand for the next 15 days

Find out the stock situation, if the owner of the bakery decides to buy 30 cakes every day. Also estimate the daily average demand for the cakes on the basis of simulated data.

3. The occurrence of rain in Delhi on a day is dependent upon whether or not it rained on the previous day. If it rained on the previous day, the rain distribution is given by:

Event | Probability |
---|---|

No. rain | 0.55 |

1 cm. rain | 0.20 |

2 cm. rain | 0.15 |

3 cm. rain | 0.05 |

4 cm. rain | 0.03 |

5 cm. rain | 0.02 |

If there was no rain on the previous day, the rain distribution is given by:

Event | Probability |
---|---|

No. rain | 0.70 |

1 cm. rain | 0.20 |

2 cm. rain | 0.06 |

3 cm. rain | 0.04 |

Simulate Delhi's weather for 10 days and determine by simulation the total days without rain as well as the total rainfall during the period.

Use the following random numbers:

48, 68, 09, 51, 56, 90, 15, 34, 68, 19

Assume that for the first day of the simulation it had not rained the day before.

4. Dr. Dang is a dentist who schedules all his patients for 30 minutes appointments. Some of the patients take more or less than 30 minutes depending on the type of dental work to be done. The following summary shows the various categories of work, their probabilities and the time needed to complete the work:

Category | Time required | Probability of categories |
---|---|---|

Filling | 45 minutes | 0.40 |

Cleaning | 15 minutes | 0.25 |

Extraction | 45 minutes | 0.15 |

Checkup | 15 minutes | 0.20 |

Simulate the dentist's clinic for five hours and determine the average waiting time for the patients as well as the idleness of the doctor. Assume that the clinic opens at 8.00 a.m.

Use the following random numbers for handling the above problem:

40, 82, 11, 34, 25, 66, 17, 79, 48, 68, 09, 51, 56, 90, 15

5. The management of Spitzen Watch company is considering the problem of marketing a new product . The fixed cost required in the project is Rs. 3,000. Three factors are uncertain viz. the selling price, variable cost and the annual sales volume. The product has a life of only one year. The management has the data on these three factors as under:

Selling Price Rs. |
Probability | Variability | Probability | Sales Volume (Units) |
Probability |
---|---|---|---|---|---|

3 | 0.2 | 1 | 0.3 | 2,000 | 0.3 |

4 | 0.5 | 2 | 0.6 | 3,000 | 0.3 |

5 | 0.3 | 3 | 0.1 | 5,000 | 0.4 |

Consider the following sequence of random numbers:

81, 32, 60, 04, 46, 31, 67, 25, 24, 10

Using the above sequence, simulate the average profit for the above project on the basis of 10 trials.