Q$2.($Inventory Buildup & Little's Law$).$ McDonald's at Coit and Turnpike is operating from $9$am to $5$ pm $.$ The restaurant can serve up to $100$ customers per hour. Customers arrive at the rate $120$ customers $/$ hour during the hours $9-1$ lam to grab McMorning, $200$ customers $/$ hour pour in during the peak hours of $11$ am to $1$ pm $,$ and for the lazy afternoon hours until the restaurant closes, only $20$ customers walk in per hour.

$($a$)$ Plot the build$-$up diagram of waiting customers at McDonald's $(3$ points$)$

Total Waiting Customers$($b$)$ What is the average number of people waiting throughout the day? $(3$ point$)$

$($c$)$ What is their average waiting time? $(3$ point$)$