Reference no: EM132859837

1. Consider a motor vehicle department that operates as follows.

Each customer sees a clerk (receptionist) to check their documents for accuracy. The service time per customer (in minutes) can take any value between 2 to 5 minutes. Then, each customer require service on (a) getting or renewing a driver's license or registering an automobile, or leave. 30% of customers get or renew a driver's license, 50% of the customers register an automobile and the remaining 20% of customers leave the service. The service time for getting or renewing a driver's license is gamma distributed with shape parameter 3 and scale parameter 10. Registering a car is a new service offered to customers in this department so the management lacks data to find the best distribution to represent the characteristics of this service. However, the experts believe that the service time is usually between 10 to 35 minutes with 20% chance of being less than 15 minutes, 60% chance of being less than 25 minutes and 95% chance of being less than 30 minutes. Labor costs are $20 per hour for the receptionist, $30 for the clerk who serve people getting or renewing their driver's license, $40 for the clerk who helps customer to register an automobile. Develop a simulation model for this system and answer the following questions:

a. What is the mean and standard deviation of the service time per customer (do not include waiting time)?

b. What is the probability that the service time per customer will be less than 8 minutes? What is the probability that the service time per customer will exceed 20 minutes?

c. What is the mean and standard deviation of the labor cost per customer to deliver this service?