RentAPhone is a service company providing European mobile phones to American visitors in Europe. The company currently has 80 phones available at Charles de Gaulle Airport in Paris. On average, there are 25 customers per day requesting a phone, and these requests arrive uniformly throughout the 24 hours the store is open. The corresponding coefficient of variation is 1. On average, customers keep their phones for 72 hours, with a standard deviation of 100 hours.

1. What is the average number of telephones the company has in its store?
2. How many customers, on average, are waiting for a phone?
3. What is the average waiting time per customer 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 will be reduced to 20 customers per day (everything else remains the same as before).

By analyzing RentAPhone's operations under different policies, we calculated the average number of phones available, estimated customer wait times, and explored the potential effects of rental duration restrictions.

The student's question concerns the operations of RentAPhone, a company that loans European mobile phones to American visitors at a Paris airport. The problem involves calculating the average inventory of phones, the average number of customers waiting for a phone, and the average waiting time per customer under a new rental restriction policy. Given that RentAPhone has 80 phones and an average of 25 customers per day, we can estimate that with an average rental period of 72 hours, approximately one-third of the phones would be returned each day, keeping the inventory stable. However, with a large standard deviation in rental times (100 hours), there will be variability in the actual number of phones available.

If the policy changes to restrict rentals to exactly 72 hours and customer requests drop to 20 per day, we can calculate that 20 new phones would be required each day. Since there are 80 phones and customers keep them for exactly 72 hours, the company would have an entire turnover of phones every three days, or roughly 26-27 phones available each day (80/3). As a result, there would be fewer phones than the number of customers requesting them. If we assume exactly 26-27 phones available and 20 requests per day, there would typically be no customer waiting, so the average waiting time per customer would be zero. However, given that there is a range for the average availability (26-27), there may occasionally be a very short wait for some customers on days when availability dips just below 20.