Lizao Zhang, owner of Lizao Zhang’s Treats, is considering the purchase of three alternative self-serve sundae machines to serve customers. The average service time for all three machines is normally distributed with a mean of 40 seconds. However, the machines differ with regard to the consistency of their service times due to stalling, resetting, etc. Machine A is so consistent that it effectively has no variability. Machine B is less reliable and has a standard deviation of 20 seconds. Machine C is the least reliable with a standard deviation of 60 seconds. Customers love their ice cream in the hot summertime and arrive in the store about every 50 seconds (Poisson arrivals). Lizao estimates the cost of waiting due to lost goodwill as 10 cents per minute of waiting. The amortized cost per customer of operating Machine A is 50 cents, Machine B is 45 cents, and Machine C is 40 cents.

(a) How long will customers wait in line (in minutes) for each machine?

(b) Calculate the total cost per customer of using each machine. Which should be purchased?