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 11 calls per hour. The arrival rate is 22 calls per hour.

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

Answer 1

Answer :

Given that :

Average no.of calls per hour = 11

Arrival rate calls per hour = 22

a)Here the no.of extension lines used in company at 90% of the calls is as follows :

Formula to calculate :

---------------> (1)

Now.the probability for the 2 of 2 servers will be busy is as below :

From 1 :

= 2 / [ 1 + 2 + 2]

= 2 / 5

= 0.4

So,here the two lines are insufficient.

Now for 3 of 3 servers will be busy is as below :

From 1 :

= 1.333 / [ 1 + 2 + 2 + 1.333]

= 1.333 / 6.333

= 0.2105

Here the 3 lines are also insufficient.

Now for 4 of 4 servers will be busy is as below :

From 1 :

Here the company requires 4 lines to handle 90% of calls immediately.It is sufficient.

b)The probability that a call receive a busy signal if 4 lines are used then the formula is as follows :

= 0.667 / [ 1 + 2 + 2 + 1.333 + 0.667 ]

= 0.667 / 6.997

= 0.09533

c) Here we need to calculate the percentage of calls that receive a busy signal with 2 extension lines is as follows :

The formula for 2 of 2 servers will be busy is as below :

= 0.4

Finally the percentage of calls = 40%