PART $1$: Saul Goodman loves a quick bite at Los Pollos Hermanos. Saul knows from Gustavo that Los Pollos receives a new customer every $3$ minutes on average $($coefficient of variation $=1)$ and on average it takes $2$ minutes $($standard deviation of this time is $2$ mins$)$ for the food to be prepared and served. The counter can serve at most one person at a time and the first arriving customer is served first.

A$)$ What is the inter$-$arrival time in minutes?

B$)$ What is the capacity of Los Pollos Hermanos? You can express your answer in either customers per minute or customers per hour.

C$)$ What is the utilization of Los Pollos Hermanos?

D$)$ What is the coefficient of variation of the service process of Los Pollos Hermanos?

E$)$ How long on average, in minutes, does Saul have to wait before getting served?

PART $2$: Gustavo runs the store for eight hours every day. An average order earns $$4$ in revenue and costs $$1$ in raw materials. The labor costs are $$160$ per day. Assume all customers that come within the $8$ hour window are served. What are Gustavo$$s average daily earnings $($revenues $$ cost$)$ in dollars? $\{$Hint: Remember all arriving customers are served.$]$ Gustavo puts in measure to reduce the standard deviation of the service $($or processing$)$ time. Now the coefficient of variation of service time is $0\mathrm{.}5.$

F$)$ When he is not serving a customer, Gustavo $$cooks his books$.$ How many minutes each day, on average, can Gustavo devote to this? $[$Hint: Think idle time which is $(1-$utilization$)...]$

G$)$ What is the new standard deviation of service time?

H$)$ How will the utilization change?

I$)$ How will the time in queue change?

J$)$Word has spread about the reduction in standard deviation, and customers are flocking to Los Pollos Hermanos. On average, $25$ customers now arrive per hour. What is the average inter$-$arrival time in minutes?