Problem Please note that this problem has eight parts. You may need to scroll the screen down, navigate left and right to see the whole problem. Clearly label your parts when answering. You are allowed maximum three files to upload for this problem. Must use pen to answer. Show all calculations/result to FOUR PLACES AFTER THE DECIMAL POINT (except when all succeeding digits are zeros) Must Show all calculations/steps. Failure to do so will result in a score of "0" even final answer is correct. Due to the COVID-19 pandemic crisis, a York Region fast-food franchise is now considering opening a drive-up window food-service operation Customers directly arrive at the service window where they place their order, pay for it, and receive their orders. Analysis of the past data indicates that, on average, cars arrive at the drive-thru at an average of one every 7.5 minutes with a Poisson probability distribution, and that the service time follows an Exponential probability distribution. The following two service alternatives are being considered: Alternative 1: - A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 6 minutes. Alternative 2 A two-server operation with a single waiting line but with two service windows and two employees. The employee stationed at each window fills the order and takes the money for customers arriving at the window. The average service time for this alternative is 6 minutes for each server 1. For each of Alternative 1 and Alternative 2, answer the following questions from (a) to (e). a What is the probability that the drive-thru system is idle? b. How many cars, on average, are waiting for service? c. What is the average time a car waits for service? d On average, how long will a car take in the drive-thru system? e. What is the probability that an arriving car will have to wait for service? Il Questions (1). (g) and (h) apply only to Alternative 1. 1 (For Alternative 1 ONLY) What is the server utilization rate? g. (For Alternative 1 ONLY) What is the probability that more than two cars are in the fast-food drive-thru system? n (For Alternative 1 ONLY) Suppose that service is automated with a constant service time What is the average number of cars in the waiting line? What is the average time that a car will stay in the system? of 6 minutes 1