Q$1)-($Jurassic Park$)$: A small video store has nine copies of the DVD Jurassic Park, in its store. There are $15$ customers every day who request this movie for their children. If the movie is not on the shelf, they leave and go to a competing store. Customers arrive evenly distributed over $24$ hours, and their arrival rate can be assumed to be following the Poisson distribution. The average rental duration is $36$ hours.$($a$)-$ What is the likelihood that a customer going to the video store will find the movie available?$($b$)-$ Assume each rental is $$5.$ How much revenue does the store make per day from the movie?$($c$)-$ Assume each customer that is not able to obtain the movie will receive a $$1$ bill. How much moneywould the store have to give out to customers requesting Jurassic Park every day?$($d$)-$ Assume the demand for the movie will stay the same for another six months. What would be thepayback time $($not considering interest rates$)$ for purchasing an additional copy of the movie at $$50?$ Consider the extra revenues related to part $($b$)$ and the potential cost savings $($part $($c$)).$