2. A & B, Inc. markets condominium time-shares in Branson, Missouri. The company sends mailers that announce that the recipient has won a free vacation, and should call a toll-free number to validate the prize. At the present time, calls are received at the rate of 50 per hour. The sales pitch given to the caller takes an average of 7 minutes, but the actual time is random and follows an exponential distribu- tion. Each sales pitch delivered produces one of three results: the customer declines (Prob. = .5), the customer visits the site but declines to buy (Prob. = .4, Loss = Rs.250), or the customer visits the site and makes a purchase (Prob. = .1, Profit = Rs. 10,000). It costs the company Rs.15 per hour to employ a salesperson. The telephone system used by the company can keep up to 10 callers on hold waiting to speak to the sales representative. Callers receive a busy signal when the system is full, and it is assumed that they will not call back.

a. What is the expected value of profit to the company when a customer receives a sales pitch?

b. What is the average service rate per hour (per sales representative)?

c. If it is assumed that the company loses the amount calculated in part

a. whenever a customer gets a busy signal, how many sales representative should the company employ?