Context: A small cafeteria serves very popular drinks and operates for 8 hours per day, 7 days per week. It charges customers $10 per drink. The data shows that customers arrive at the caf at an average of one every 5 minutes. The caf employs one staff, and, on average, it takes 4 minutes for the staff to serve each customer (from taking the order and the payment as well as making the drink). The hourly salary of the staff is $25. (Assume a Poisson distribution for the arrival rate of customers and exponential distribution for the service time performed by the staff).

Question: The management considers three options to reduce the customers' waiting time:

(i)Employing another staff just to take the order and payment while the original staff will make the drink only. This option will reduce the service time by 50%.

(i)Employing another staff (with a similar level of skills to the original staff) to perform the full service to customers.

(ii) Replacing the staff with an automatic machine with an average service time of 4 minutes per serve (assume normal distribution). The automatic machine costs $20,000.

Calculate the average customers' waiting time for each of the three options