Mandy operates a coffee stand. Customers arrive randomly at a mean rate of $20$ per hour. The time needed by Craig to serve a customer has an exponential distribution with a mean of $90$ seconds.

Create an Excel model of this situation to help you answer the following questions:

$1)$ What is the utilization of the system?$(1)$

$2)$ What are the value of$$L$,$ Lq$,$ W$,$ and Wq$?(1)$

$3)$ What is the probability that exactly $5$ people are waiting in the system?$(1)$

$4)$ What is the probability that less than $2$ people are waiting in the system?$(1)$

$5)$ If each the cost of waiting is determined to be $$200$ per hour $($since customers will just leave if they wait too long$)$ and servers cost $$18$ each, what is the optimal number of servers based on economic analysis?$(1)$