Road Rambler sells specialty running shoes and apparel through catalogs and the Web. Customers can phone in orders at any time day or night, seven days a week. During the 4 am to 8 am shift, a single sales rep handles all calls. During this time, calls arrive at a rate of 14 per hour following a Poisson distribution. It takes the sales rep an average of four minutes to process each call. The variability in service times is approximately exponentially distributed. All calls received while the sales rep is busy are placed in a queue.
a. On average, how long (in minutes) must callers wait before talking to the sales rep?
b. On average, how many customers are on hold?
c. What is the probability that the customer will be placed on hold?
d. What is the sales rep’s utilization rate?
e. Suppose Road Rambler wants there to be no more than a 10% chance that a customer will be placed on hold. How many sales reps should the company employ?