Consider an auto assembly line where engines are first installed and then tires are put on cars. An average of 54 cars per hour arrive requiring these two tasks. One worker is available to install the engine and can serve an average of 60 cars per hour. After the engine is installed at the engine station, the car goes to the tire station and waits for its tires to be attached. Multiple workers serve at the tire station. Each works on one car at a time and can put tires on a car in an average of 3 minutes. Both interarrival times and service times are exponential. a Assume that it costs $10 per hour to hire a worker working at the tire station, and it will lose $50 for each hour that a car waits in line. (1) (30%) How many workers should be hired working at the tire station to minimize the total expected hourly cost? Please show your analysis to justify your answer. (2) (10%) For the optimal number of workers at the tire station found in (1), determine the mean queue length at each workstation. (3) (10%) For the optimal number of workers at the tire station found in (1), determine the total expected time that a car spends waiting for service