Mid-West Publishing Company publishes college textbooks. The company operates an
ID: 449661 • Letter: M
Question
Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour.
How many extension lines should be used if the company wants to handle 85% of the calls immediately?
What is the probability that a call will receive a busy signal if your recommendation in part (a) is used? If required, round your answer to four decimal places.
What percentage of calls receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.
Explanation / Answer
mu = 16 calls per hour and lambda = 10 calls per hour
Answer-1 Here rho = p = effitiency of the system = 10 / 16 = 0.625
this is the effitiency with two representatives handling the calls
if effitiency = 85% then in this case number of reprenetatives required = 3
Answer-2 The probability = 1 - lambda / mu = 1- 0.85 = 15%
Answer-3 In the current system
probability that the busy signal would come = 1 - 10/16 = 1- 0.625 = 0.375 = 37.5%