Pittsburgh Cab Company uses two dispatchers to handle requests for service to dispatch cabs. The telephone calls are made to Pittsburgh Cab using a common telephone number. When both dispatchers are busy, the caller hears a busy signal; no waiting is allowed. Callers who receive a busy signal can call back later or call another cab service. Assume that the arrival of calls follows a Poisson probability distribution with a mean of 40 calls per hour. Assume each dispatcher can handle an average of 30 calls per hour. The company has hired you, as a consultant, to answer the following questions:

1. What percentage of time are both dispatchers idle? 2. What percentage of time are both dispatchers busy? 3. What is the probability that callers will receive a busy signal if two, three or four dispatchers are used? 4. Suppose management wants no more than 12% of callers to receive a busy signal. How many dispatchers should be used? 5. Suppose a new management team comes in and wants no more than 7% of callers to receive a busy signal. How many more dispatchers will need to be hired?

Report your results in a table and discuss them. What are important costs for the company to consider?