$1.($Total $12$ pts$)$ A take away burger restaurant has just opened a new branch operating nearby UCSD's campus downtown. The restaurant operates in line with the following flowchart: $-$ Over the first two weeks in operation, the restaurant has remained open from $9$am$-5$pm dailv, and has seen a relatively consistent average of $80$ customers per day. On average, $|$ the first queue has approximately $5$ people. $-$ Since the menu and restaurant are relatively new, patrons will need to inquire about the various options available, and will typically spend approximately $5$ minutes placing an order. $-$ Immediately after placing their order, customers will then join another queue to collect their food, which on average has $3$ people in line. The average service time to collect food once someone arrives at the counter is $1\mathrm{.}5$ minutes. $-$ Since the restaurant and staff are new to the business, some customers $($on average $15\%)$ will need request a change to their order. This can be done at the station, and typically takes $20$ minutes. There is no queue for this process.a$)(3$ points$)$ How long does an average customer spend in the queue before they are able to order food? b$)(3$ points$)$ On average, how many customers are placing their order at the counter? c$)(3$ points$)$ On average, how many minutes does a customer stay in the food collection queue? d$)(3$ points$)$ On average, how many customers are being served at the food collection counter?