Advanced Clock Repair Services repairs a large variety of antique clocks. Dennis, the owner, operates the business out of his living room and he performs all repairs. Based upon history, the time to repair a clock is exponentially distributed with a mean of about 5 days. Currently, Dennis will always accept a clock for repair no matter how many are already in his living room. Customers drop off clocks for repair according to a Poisson process with a rate of about 0.18/day. Dennis charges an average of $250 for a repair. Required:
a. How many clocks would you expect to find in Dennis's living room at any time?
b. Assume you just dropped off a clock for repair. How long would you expect to wait before your clock is repaired?
c. What is Dennis's expected income rate?
d. Dennis's wife is irritated with the number of clock in the living room. Dennis is considering setting a limit of 5 clocks in his living room at any time (.e. an arriving customer will be turned away if there are already 5 clocks there). Dennis would like to determine the impact on his income rate for the new policy vs. the old. Build a model and use it to answer his question.