MidWest Publishing Company publishes college textbooks The c

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 13 calls per hour. The arrival rate is 25 calls per hour.

a. How many extension lines should be used if the company wants to handle 90% of the calls immediately?

b. 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.

c. What number of calls, in decimal form, receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.

Solution

the company operates 800 telephone numbers

so if they get 800 calls then thr representatives need to attend to a maximum of 90% of the calls immediately

=> 90% of 800 = .9*800 = 720 calls need to be aswered

and we are given that 1 representative can accomodate an average of 13 calls per hour

and 1 representative means 1 extension line is in use

=> to accomodate 720 calls the Mid-West Publishing Company would require = 720/13 extension lines

                                                                                                                                              = 55.38 or 56 extension lines