Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll$-$free

telephone number to book pizzas at any of its outlets. If the clerk is occupied on one line,

incoming phone calls to the restaurant are answered automatically by an answering machine and

asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and

answered first. Calls come in at a rate of about $15$ per hour. The clerk is capable of taking an

order in an average of $3$ minutes. Calls tend to follow a Poisson distribution, and service times

tend to be exponential. The clerk is paid $$20$ per hour, but because of lost goodwill and sales,

CWD loses about $$50$ per hour of customer time spent waiting for the clerk to take an order.

Skyline is considering adding a second clerk to take calls. The store would pay that person the

same $$20$ per hour.

Using appropriate formula for the multiple channel model, answer the following questions:

a$)$ What is the probability that no customers are in the system $($Po$)?$

b$)$ What is the average number of customers waiting for service $(Lg)?$

c$)$ What is the average number of customers in the system $($L$)?$

d$)$ What is the average time a customer waits for service $(Wg)?$

e$)$ What is the average time in the system $($W$)?$

f$)$ What is the probability that a customer will have to wait for service $($Pw$)?$

g$)$ What is the probability that there is exactly $2$ customers in the system

h$)$ Should it hire another clerk? Explain by showing the cost savings