OPRE $3310$: Homework $2($subbuit before sep$22=2024,2359pm,$ on E$-$teaming$)$

Q$1(10$ points$)$ Consider a bar that operates between $5$ pm and $3$am$.$ The demand rate is

variable, and can be described as follows:

Between $5$pm and $9$pm$,$ the demand rate is $100$ customers$/$hr

Between $9$pm and $11$ pm $,$ the demand rate is $200$ customers$/$hr

Between $11$ pm and $1$ am$,$ the demand is constant and equal to $50$ customers$/$hr

After lam, no new customers arrive

To serve this demand, the bar has bartenders that work on different shifts. The restaurant

knows that each bartender has a capacity of $50$ customers$/$hour$,$ and suppose that the

bartenders can serve customers in parallel. In addition, we know that:

Between $5$pm and $8$pm$,$ there is only one bartender working at the restaurant

After $8$pm$,$ and until the bar closes, there are two bartenders working in phrallel

$($a$)$ Plot the evolution of the demand rate and the service rate $($or capacity$)$ of the

restaurant. $($S points$)$

$($b$)$ Draw the inventory build$-$up diagram. $(5$ points$)$