7.7 A company is considering how much capacity K to provide in its new service facility. When the facility is completed, customers are expected to arrive at the facility according to a Poisson process with a mean rate of 10 customers per hour, and customers that arrive when the facility is full are lost. The company hopes to hire an attendant to serve at the facility. Because the attendant is to be paid by the hour, the company hopes to get its money’s worth by making sure that the attendant is not idle for more than 20% of the time he or she should be working. The service time is expected to be exponentially distributed with a mean of 5.5 min.

a. How much capacity should the facility have to achieve this goal?

b. With the capacity obtained in part (a), what is the probability that an arriving customer is lost?