Instruction: For all questions, a) first state parameters given. b) The state the applicable formula c) Plug inte the formula d) Solve and state answer in three decima place e) State units for your answer QUESTION \#1 A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intereom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered: - 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 2 minutes. -A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes. - A two-server operation with two serviee 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 2 minutes for each service. Answer the following questions and recommend one of the design options. a. What is the probability that no cars are in the system? b. What is the average number of ears waiting for service? c. What is the average number of cars in the system? d. What is the average time a car waits for service? e. What is the average time in the system? f. What is the probability that an arriving car will have to wait for service? SOLUTIONS Arrival rate (Q)=24 cars per hour, 2 mins per car Customer rate ()=1/2 cars per mins The utilization factor ()