Question: Mike operates a hair-cutting salon that specializes in providing quick walk-in service for just about any type of haircut. He deals with customers as they walk in the door. This includes writing down the customer's name and what they desire in terms of haircut, wash, dry, and so on. This process usually takes two minutes. If no hair stylist is available, the customer then goes to the waiting area, where he/she is processed on a first-come, first-serve basis. The salon has five hair stylists who work eight hours each day. It takes, on average, 25 minutes for a stylist to greet the customer, wash and/or cut his hair, and wish him a fond farewell. Then Mike completes the process by taking the customer's money and telling him about the satisfaction guarantee offered by the shop. This final set of steps takes two minutes on average.
a. Assuming that the waiting area always has at least one customer in it, how many customers on average can Mike's salon process in a day (assuming no problems in utilization, quality, or efficiency)?
b. Suppose that you need an "average" haircut, and as you walk into the salon you see three people sitting in the waiting area. You notice that another person is just sitting down in one of the stylists' empty chair, and the other stylists are all busy with customers. Assuming you choose to wait, how long would you expect it to be before you are ready to leave the salon?