The Debbie Dollar Income Tax Specialists are analyzing customer service operations during the month prior to the April filing deadline. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with an average arrival rate of one every 12 minutes. The time to complete a return for a customer is exponentially distributed with a mean of 10 minutes. When the person is being helped, he meets with Debbie in her office. If the individual is waiting for help, he will be in the waiting area. Based on this information, answer the following questions.
Do not round your results to integer numbers.
a) If you went to Debbie, how much time should you allow for getting your return done? Measure this time from when you first arrive at her office.
b) On the average, how many customers should the waiting area be designed to hold?
c) What is the probability that an arriving customer would find at least two other people in the waiting area waiting for help?
d) At this time, Debbie is not going to add another person to help complete the tax returns. If the arrival rate remains unchanged but the average time in the system must be 40 minutes or less, what would need to be changed and what would the value of the change need to be?
e) Debbie is now considering adding a person to help her process the tax returns. This person will help Debbie by checking the paper work for the customers. Debbie believes that this will allow her to complete the returns in six minutes 40 seconds on average. Debbie would need to pay this person $50 per hour. Debbie believes that she has to reduce her cost of the service by $15 per hour for every hour a customer is in her office either waiting for help or being helped. Should Debbie add this person or continue working by herself? Base your analysis on the economics of the two options.