You own a big rental car company in Indianapolis and maintain a fleet of 50 SUVs. Customers make their rental car reservations using an app before they arrive the location, and therefore, as long as a car is available in the lot they directly proceed to the car assigned them through the app for pick up. If all SUVs are rented, your customers are willing to wait until one is available. The average time between requests for an SUV is 2.5 hours, with a standard deviation of 2.5 hours. The arrival pattern remains to be consistent throughout the day (24 hrs). An SUV is rented, on average, for 4 days with a standard deviation of 1 day.

a) At any given time, what is the average number of SUVs parked in your company's lot? (Hint: you need to find the average number of SUVs rented and then subtract this number from the fleet size, i. e., 50. Make sure the time units match in your calculations.).
b) What is the average time a customer has to wait before getting a rental SUV (in (mins])?
c) ** You make a marketing survey and find that if you reduce daily rental price from $60 to $45, the average rental duration would become 5 days. What is the minimum demand rate [customers/day) that would justify the price decrease? (Assume that Va and CVp do not change). (Hint: You need to find how much you would make per day with the current pricing, i. e., Ip*$60/day, let's call it X for now. Then find how much you would make under the new pricing as a function of interarrival time [here, remember that rental duration changes). Then solve for the interarrival that gives a profit at least as high as X. Use this inter-arrival time you found to calculate the demand rate).
d) You are considering making a change on rental policy by limiting all SUV rentals to exactly 4 days. If you impose this restriction, the average interarrival time will go up to 3 hours and the standard deviation will become 3 hours. What would the waiting time be after this change in rental policy?