A small video store currently has 9 copies of the DVD I'm Number 4 in its store. There are 15 customers on average every day coming to the store to request this movie. If the movie is not on the shelf, they leave and go to a competing store without waiting. The average rental duration is 36 hours. Each rental is $5 (i.e., $5 per rental for the whole rental period, not per day).
a) What is the probability that a customer going to the video store will find the movie available?
b) How much revenue does the store make per day from this movie?
c) Assume the demand for the movie will stay the same for a sufficiently long time. It costs $50 to purchase a copy of this movie. Suppose this video store plans to buy a new copy and then there will be total 10 copies of this movie. What will be the payback time for this $50 investment?