$(30$p$.)$ Build the simulation by using ARENA. Please share the arena file Insread of writing theoritical. A popular dancing club, which opens at $9$:$00$ pm and closes at $3$:$00$ am$,$ has two dance floors each with a capacity of $20$ people, but the second floor closes after $00$:$00.$ The club receives customers only as couples and it does not accept the single person entry. If the club is full, a newly arrived couple waits in front of the club's door. Assume that each couple dances at least $30$ minutes and at most $90$ minutes. The mean time between arrivals is $10$ minutes between $21$:$00-00$:$00,20$ minutes between $00$:$00-01$:$00,$ and $30$ minutes between $02$:$00-03$:$00.$ Assume the memoryless property for the inter$-$arrival times. $10\%$ of arriving couples are VIP customers who does not wait in the queue of regular customers. If the club is full, VIP customers leave without waiting. Assume that the dancing time of a VIP couple follow a triangular distribution with parameters $30,50,$ and $100$ minutes.

Build a simulation model to answer below questions.

a$.$ What is the probability that the queue will be longer than $5?$

b$.$ What is the probability that a person will wait more than $10$ minutes in the queue?

c$.$ If the second floor remains open after $00$:$00,$ how above probabilities will change? Is it sensible to keep the second floor open after $00$:$00?$