After graduating from Georgia Tech, you open Yellow Jacket Home Renovations, a home renovation company that focuses on full renovations of midcentury modern homes in the greater Atlanta region. You estimate that the revenue you make per renovation is $250,000. Your first business decision is to choose how many full-time renovation crews you will hire. A renovation crew is a small team of workers responsible for renovating one house. To keep things simple, once a renovation crew is allocated to a house, they work on its renovation until it is completed. If there are fewer home renovation requests at any given time than renovation crews, some renovation crews will be idle until more requests come in. Conversely, if all renovation crews are busy and a home renovation request from a customer arrives, that customer will wait in a queue until a renovation crew becomes available. After gathering some data, you estimate that a renovation crew takes about four months on average to renovate a home. The time it takes to renovate a home has uncertainty, and you estimate that the standard deviation of the renovation time is three months. Furthermore, customers are impatient. If a customer arrives and sees that their average wait time until their home renovation begins is longer than three months (i.e., their average wait time is longer than three months), they will leave and write a terrible review on Google and Yelp. You want to avoid bad reviews as much as you can.

Question 1 Your initial revenue goal is to have an average revenue of $2,000,000 per year (i.e., an average of 8 home renovations per year). Assume that the coefficient of variation of the inter-arrival time of customers requesting renovations is 1. Given your annual revenue goal, what is the minimum number of renovation crews you need to hire such that customers' average wait time for their renovation to start is less than three months?

Question 2 For your answer in the previous question, what will your renovation crews average utilization be? What is the average number of customers in the system (customers waiting for renovation to start + customers having their home renovated)? What is the average annual revenue per renovation crew?