Problem #$3[40$pts$]$

You are modeling a sit down restaurant:

Customers $($really groups of customers needing a single table$)$ arrive at the restaurant at a rate of

$50$ groups per hour. No groups are seated after $8$:$30$pm$.$

Customers are not willing to wait forever to get a seat. Customers will wait $Triangular(5,15,40)$

minutes before deciding to leave and look for another place to eat. Send reneging customers to a

"Sink$2"$ so you can visually see them leaving.

The restaurant has $30$ tables. Assume any group can be seated at any available table. Service time

for each group is $NORM(70,15)$ minutes.

Add status plots showing the number of tables in use and the number of reneging

customers so far. Run interactively to see behavior $($suggest speed factor of $7$ to $8)$

To answer the following questions, run $30$ replications of an evening shift $5-10$pm $($with

no warmup$).$

Document the following in the Word doc:

$\%$ utilization of the tables

How many customer groups were served on average over the evening shift?

On average, what was the wait time for customer groups before being seated?

On average, how many customer groups reneged? What percentage of all arrivals reneged?

Suppose it costs $$\frac{6}{h}r$ for each additional table added to the restaurant $($assume space is

available$).$ The profit per customer group served is $$75.$ Is it worthwhile to add additional tables?

Justify your answer.