Question 6: (12 points) Jim Wood, a mechanic working for Forest, is able to install new mufflers on the average about one every 6 minutes, following the exponential distribution. Customers needing this service arrive at the shop on the average of 4 per hour, following a Poisson distribution. Tim Forest, the shop owner, would like to evaluate several alternatives of the waiting lines system. He estimates that the cost of customer waiting time, in terms of customer dissatisfaction and lost goodwill, is $30/hour of time spent waiting in line. The pay rate of Wood is $20/hour. Forest is considering the following two alternatives for process and cost improvement: Option 1: Replacing Jim Wood with Kim Meadow who can efficiently install new mufflers averagely 5 minutes each, but will be paid at $24/hour. Option 2: Installing a new automated machine to install mufflers rather than hire the mechanic. The machine can install mufflers at a constant time, 8 minutes per car. The cost of purchasing and operating the new machine will be amortized at a rate of $4 per car it serves. 1) Calculate the total cost (waiting and capacity) per hour, and the utilization for Option with Jim, Options 1 and 2. 2) If you were the manager of this repair shop, which alternative (with Jim, option 1, or optimal 2) would you implement? Explain your reasoning and justify quantitatively