Please solve in excel and show excel steps. The Judy Gray Income Tax Service is analyzing its 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 $5$ per hour. The time to complete a return for a customer is exponentially distributed with a mean of $10$ minutes.

Assume that the customer has all of the information needed for Judy to complete the tax return at

this one visit. When the person is being helped, she meets with Judy in her office. If the

individual is waiting for help, she will be in the waiting area. Based on this information, answer

the following questions.

Do not round your results to integer numbers.

a$)$ On the average, how many customers should the waiting area be designed to hold?

b$)$ What is the probability that an arriving customer would find at least two people in the waiting

area waiting for help?

c$)$ Judy is now considering adding a person to help her process the tax returns. This person will

help Judy by checking the paper work for the customers but does not work directly with any

customer. Judy believes that this will allow her $($Judy$)$ to complete the returns in six minutes $40$

seconds on average. Judy would need to pay this person $$50$ per hour. Judy believes that she

has to reduce her cost of the service by $$15($cost of waiting$)$ per hour for every hour a customer

is in her office either waiting for help or being helped. Should she add this person or continue

working by herself? July does not reveal how much she pays herself $($zero$).$

Base your analysis on the economics of the two options.

Note: since Judy$$s cost is a constant, we can ignore this in the calculations