1. The airport branch of a car rental company maintains a fleet of 30 SUVs. The inter-arrival time between requests for an SUV is 2 hours with a standard deviation of 2 hours. Assume that, if all SUVs are rented, customers are willing to wait until an SUV is available. An SUV is rented, on average for 2 days, with a standard deviation of 1 day. Assume the car rental is open 24 hours a day. a) What is the average number of SUVs parked in the company's lot?
b) Through a marketing survey, the company has discovered that if it reduces its daily rental price of $80 by $25 (for this part only), the average demand would increase to 12 rental requests per day and the average rental duration will become 4 days. Is the price decrease warranted?
c) What is the average time a customer has to wait to rent an SUV? Please use the initial parameters rather than the information in (b).
d) How would the waiting time change if the company decides to limit all SUV rentals to exactly 4 days? Assume that if such a restriction is imposed, the average interarrival time will increase to 3 hours, with the standard deviation changing to 3 hours.
2. Atlantic Video, a small video rental store in San Diego, is open 24 hours around the clock. A recent analysis done by the store manager indicates that there are 30 customers every hour, with a standard deviation of inter-arrival times of 2 minutes. This arrival pattern is consistent and is independent of the time of day. The checkout currently operated by one employee, who needs on average 1.7 minutes to check out a customer. The standard deviation of this check-out time is 3 minutes, primarily as a result of customers taking home different numbers of videos.
a) If you assume that every customer rents at least one video (i. e. has to go to check out), what is the average time a customer has to wait in line before getting served by checkout employee, not including the actual checkout time?
b) If there are no customers requiring checkout, the employee is sorting returned videos, of which there are always plenty waiting to be sorted. How many videos can the employee sort over 8-hour shift if it takes exactly 1.5 minutes to sort a single video?
c) What is the average number of customers who are at the checkout desk, either waiting or currently being served?