Question 3 (2+2+3+3+5 = 15 points) Atlantic Video, a small video rental store in Philadelphia, is open 24 hours a day, and-due to its proximity to a major business school-experiences customers arriving around the clock. A recent analysis done by the store manager indicates that there are 30 customers arriving every hour, with a standard deviation of interarrival times of 2 minutes. This arrival pattern is consistent and is independent of the time of day. The checkout is currently operated by one employee, who needs on average 1.5 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 the checkout), what is the average time a customer has to wait in line before getting served by the checkout employee (i.e., waiting time in queue)? 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 an 8-hour shift (assume no breaks) if it takes exactly 1.5 minutes to sort a single video? Hint: similar to part (a) in Question 2 c. What is the average number of customers who are at the checkout desk, either waiting or currently being served? d. Now assume for this question only that 10 percent of the customers do not rent a video at all and therefore do not have to go through checkout. What is the average time a customer has to wait in line before getting served by the checkout employee (i.e., waiting time in queue)? Assume that the coefficient of variation for the arrival process remains the same as before. Hint: Arrival rate becomes 90% of current arrival rate. You need to calculate the interarrival time for this new arrival rate. e. As a special service, the store offers free popcorn and sodas for customers waiting in line at the checkout desk. (Note: The person who is currently being served is too busy with paying to eat or drink.) The store owner estimates that every minute of customer waiting time costs the store 75 cents because of the consumed food. What is the optimal number of employees at checkout? Assume an hourly wage rate of $10 per hour, and all customers need to check out (i.e., disregard part (d)). Hint: Tradeoff between the cost of hiring employees and that of customer waiting (food consumption). Consider a one hour period, the total cost includes customer waiting cost (average number of customers in queue, times 75 cents per customer per minute, time 60 minutes per hour) and employee wages ($10 per hour per employee times the number of employees). Calculate the total cost when you hire 1, 2, 3, or 4 employees and choose the one with the lowest total cost.