A restaurant’s reservation agent takes reservations for dinner by telephone. If he is already on the phone when a patron calls to make a reservation, the incoming call is answered automatically, and the customer is asked to wait for the agent. As soon as the agent is free, the patron who has been on hold the longest is transferred to the agent to be served. Calls for reservations come in at a rate of about 15 per hour. The agent is able to make a reservation in an average of three minutes. Calls tend to follow a Poisson distribution, and the times to make a reservation tend to be exponential. The agent is paid $15 per hour. The restaurant estimates that every minute a customer must wait to speak to the agent costs the restaurant $1.
(a) What is the average time that diners must wait before their calls are transferred to the agent?
(b) What is the average number of callers waiting to make a reservation?
(c) The restaurant is considering adding a second agent to take calls, who would be paid the same $15 per hour. Should it hire another agent? Explain.