Furry Friends is a new service company that provides pets to Hospitals. The company currently has 85 animals. There are, on average, 20 customers per day requesting a pet. 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 pets for 72 hours on average. The standard deviation of this time is 100 hours.
Given that Furry Friends currently does not have a competitor providing equally good service, customers are willing to wait for the pets. Based on prior experiences, Furry Friends found that the company incurred a cost of $1 per hour per waiting customer, independent of day or night.
a. What is the average number of pets the company has in its store?
b. How long does a customer, on average, have to wait for the Pet? (in Hours)