Q$8\mathrm{.}6($RentAPhone$)$ RentAPhone is a new service company that provides European mobile phones to American visitors to Europe. The company currently has $80$ phones available at Charles de Gaulle Airport in Paris. There are, on average, $25$ customers per day requesting a phone. These requests arrive uniformly throughout the $24$ hours the store is open. $($Note: This means customers arrive at a faster rate than $1$ customer per hour.$)$ The corresponding coefficient of variation is $1.$

Customers keep their phones on average for $72$ hours. The standard deviation of this time is $100$ hours. Given that RentAPhone currently does not have a competitor in France providing equally good service, customers are willing to wait for the telephones. Yet, during the waiting period, customers are provided with a free calling card. Based on prior experience, RentAPhone found that the company incurred a cost of $$1$ per hour per waiting customer, independent of day or night.

What is the average number of telephones the company has in its store?

How long does a customer, on average, have to wait for the phone?

What are the total monthly $(30$ days$)$ expenses for telephone cards?

Assume RentAPhone could buy additional phones at $$1,000$ per unit. Is it worth it to buy one additional phone? Why?

How would waiting time change if the company decides to limit all rentals to exactly $72$ hours? Assume that if such a restriction is imposed, the number of customers requesting a phone would be reduced to $20$ customers per day.