A small video store currently has 10 copies of the DVD I’m Number 4 in its store. There are 7 customers on average every day coming to the store to request this movie. The average rental duration is 1 day (i.e., 24 hours). Each rental is $5 per rental. If the movie is not on the shelf, the store discounts rental fee $1 per waiting hour (e.g., if a customer waits for 1.5 hours, then s/he needs to pay only $3.5.). We assume customers wait until they can rent the DVD.
(a) How long does a customer wait on average?
(b) What is the profit of the store from this movie per day?
(c) Assume the demand for the movie will stay the same for a sufficiently long time. It costs $100 to purchase a copy of this movie. Suppose this video store plans to buy a new copy and then there will be total 11 copies of this movie. What will be the payback time for this $100 investment?