1. Atlantic Video, a small boutique video rental store in Los Angeles, is open 24 hours a day, and its customers arrive around the clock. A recent analysis done by the store manager indicates that there are on average 30 customers arriving every hour, with a standard deviation of inter-arrival time of 2 minutes. This arrival pattern is amazingly consistent and is independent of the time of day. There is one check-out line 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 choosing different numbers of videos.a. If we assume that every customer rents at least one video (i.e., has to go thru the check-out), what is the average time a customer has to wait in line before getting served by the check-out employee (this doesn’t include the actual check-out time). Include the image of your Excel solution. You can use an exact or approximate calculation.b. If there are no customers requiring check-out, the checker will sort returned videos during that idle time; there are always plenty waiting to be sorted. How many videos can the checker expect to be able to sort, on average, over an 8-hour shift (assume no breaks) if it takes exactly 1.5 minutes to sort a single video?c. What is the average number of customers who are at the check-out desk, either waiting or currently being served?d. Suppose we now discover that 10 percent of the arriving customers do not rent a video at all, and therefore do not have to go through check-out. So the arrival rate to the checker is actually only 90% of what we used earlier. What is the average time a customer has to wait in line before getting served by the check-out employee, not including the actual checkout time? Assume that the coefficient of variation for the arrival process remains the same as before.
