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.

1. 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.
2. 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.
3. How many extension lines should be used if the company wants to handle 85% of the calls immediately?

Answer 1

Solution:-

Given that,

A)

For two extension lines,percentage of calls that will receive a busy signal

Answer=30%.

B)

As already calculated;If part(a) is used

C) Calculation of the number of lines to be used

By using the below formula,we will get the busy time:

Niw comapare probability

given that,

and take k=2 for 2 series.

So,2 lines are not enough.

Consider 3 lines now,

26%busy time.

4 Extension lines must be used.

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(a) 3 lines are to be used

(b) 0.26

(c) 30.00%