A local caf has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival time an average of one every 2 minutes. The time to place their order and pay at the register is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customers order is then passed to one of the servers who take on average 5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order. a. Calculate the capacity of the register and the servers. What is the bottleneck in this system? b. Calculate the average utilizations of the register and the servers c. What is the probability a customer is delayed at the register? d. What is the expected time from a customers arrival to the order being passed on to the servers (including any queueing time)? e. Estimate the probability that there is a delay between a customer placing his order and a server beginning to work on the order.