Problem 1: Single Server Model. A cafeteria can seat a maximum of 50 persons. Customers arrive in a Poisson distribution at the rate of 10 per hour and are served (one at a time) at the rate of 12 per hour. Show your solutions manually, showing all the units in your computation process. Check your answer using the Excel Computation formula I have sent to you. Submit your work (manual computations and excel computations). a). What is the average time each customer spent in queue? b). How many customers are there in the waiting line at any given time? c). What is the average time each customer spent in the system d). How many customers are there in the system at any given time? e). What is probability that the service facility is idle? f). What is the utilization factor of the service facility g). What is the probability that there will be 10 customers in the system h). What is the probability that an arriving customer will not eat in the cafeteria because it is full? i).Suppose that three customers (with random arrival times) would like to be seated together. What is the probability that their wish can be fulfilled? (Assume that arrangements can be made to seat them together as long as three seats are available)