Question $2$: Inventory Build$-$up and Little's Law II

The capacity of a fast$-$food outlet is $130$ customers an hour during peak hours, and $65$ customers an hour during normal hours. The outlet operates $24$ hours a day, Seven days a week. The rate of demand is $156$ customers per hour during the peak demand period $12$:$00$ to $1$:$00$ PM $($noon$)$ daily, and $52$ customers per hour in other times.

Part a: $2$ points

How many customers are at the fast$-$food outlet at $1$:$00$PM$?$

Locally stored answer:

Part b: $4$ points

How long does the customer that arrives at $1$ PM should wait before being served? Please provide your answer in minutes.

Locally stored answer:

Part c: $2$ points

At what time will the peak hour congestion be over, i$.$e$.,$ inventory reduces to zero? Please state the hour as a single number.

Locally stored answer:

Part d: $4$ points

What is the average flow time of a customer in minutes from $12$:$00$ to $3$:$00$ PM$?$

Locally stored answer:

Part e: $4$ points

The outlet manager manger decided to maintain the capacity at $130$ customers per hour for one hour beyond the peak hour $($i$.$e$.,$ until $2$:$00$PM$).$ What is the $($new$)$ maximum wait time in minutes?

Locally stored answer: