Question $1(20$ points $5$ points per part$)$

Matthew the Barber owns a one$-$chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of $20$ minutes to give a haircut. Based on these figures, find thefollowing:

Part $($a$)$: The average number of customers waiting: $1\mathrm{.}33$

Part $($b$)$: The average time a customer waits.: $40$ mins

Part $($c$)$: The average time a customer is in the shop: $60$ mins

Part $($d$)$: The average utilization of Matthew$$s time: $67\%$

Find me the answer for Question $2$ Also include steps and formula please double check the work. Question $1$ i have already given

Question$2$:

Matthew the Barber $($see Question $1)$ is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from those waiting. Matthew has assumed that both barbers would take an average of $20$ minutes to give a haircut, and that business would remain unchanged with customers arriving at a rate of two per hour. Find the following information

to help Benny decide if a second chair should be added:

Part $($a$)$: The average number of customers waiting. $?$

Part $($b$)$: The average time a customer waits. $?$

Part $($c$)$: The average time a customer is in the shop. $?$