Jasper Valley Motors (JVM) is a mid-sized, family-run auto repair shop. To assure customer satisfaction, JVM has kept a fleet of four "loaner" cars that customers may drive while their vehicles are being serviced. In an average week, 15.5 major repairs are scheduled for which owners request a loaner car (the service department is open five days per week). Of course, the exact number of loaner requests is random, and the time between requests may be assumed to be exponentially distributed. If a loaner car is not available when a customer needs one, JVM's policy is to take $50 off the cost of the service as compensation for the customer inconvenience, as they must find alternate transportation to and from the shop. Most repairs are done within a day but some take longer, requiring the customer to keep the loaner car for several days. It has been observed that on average, a customer keeps a loaner car for 1.2 days, and the actual time may be assumed to be exponentially distributed.
a.What is the probability that a customer who requests a loaner car from JVM will actually get one?
b. What is the percentage utilization of JVM's fleet of loaner cars? On an average day, how many loaner cars are on JVM's lot (i.e., not loaned out to customers)?
c. Suppose JVM leases the loaner cars from an automaker at a rate of $350 per month per car, which includes insurance. Max estimates that it costs $12 per "loaner", which covers the cost of the necessary paperwork when the car goes out as well as cleaning the car when it is returned. What are JVM's monthly costs of running the loaner car program (including discounts to those who do not receive loaners)? Assume 20 days in a month.

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The Answer of Jasper Valley Motors (JVM) is a mid-sized, family-run auto repair shop. To assure customer satisfaction, JVM has kept a fleet of four "loaner" cars that customers may drive while their vehicles are being serviced. In an average week, 15.5 major repairs are scheduled for which owners request a loaner car (the service department is open five days per week). Of course, the exact number of loaner requests is random, and the time between requests may be assumed to be exponentially distributed. If a loaner car is not available when a customer needs one, JVM's policy is to take $50 off the cost of the service as compensation for the customer inconvenience, as they must find alternate transportation to and from the shop. Most repairs are done within a day but some take longer, requiring the customer to keep the loaner car for several days. It has been observed that on average, a customer keeps a loaner car for 1.2 days, and the actual time may be assumed to be exponentially distributed.
a.What is the probability that a customer who requests a loaner car from JVM will actually get one?
b. What is the percentage utilization of JVM's fleet of loaner cars? On an average day, how many loaner cars are on JVM's lot (i.e., not loaned out to customers)?
c. Suppose JVM leases the loaner cars from an automaker at a rate of $350 per month per car, which includes insurance. Max estimates that it costs $12 per "loaner", which covers the cost of the necessary paperwork when the car goes out as well as cleaning the car when it is returned. What are JVM's monthly costs of running the loaner car program (including discounts to those who do not receive loaners)? Assume 20 days in a month.

Jasper Valley Motors (JVM) Is a Mid-Sized, Family-Run Auto Repair