A firm that prints affordable college and high textbooks to local schools here in South Florida. He has a $800$ toll$-$free telephone number that teachers, professors and librarians can call when thinking about adopting new books, or review copies of new materials, and also to place orders. Currently, Hehas two extension lines to the number which are manned by two representatives who answer the phone inquiries. Calls occurring when both representatives are busy on the phone receive a busy signal, and there is no waiting allowed in the system. Each representative can accommodate an average of $12$ calls per hour. The mean arrival rate is $20$ calls per hour. Assume the calls follow Poisson arrival distribution and the service rate is exponentially distributed.

$1.$ How many extension lines should be used if the company wants to handle $90\%$ of the calls immediately? $(4$ point$)$

$2.$ What is the average number of extension lines that will be busy if your recommendation above is used? $(4$ point$)$

$3.$ What percentage of calls receive a busy signal for the current telephone system with two extension lines? $(4$ point$)$