Gerard Is Choosing Between Two Methods of Organizing His Bakery

Gerard is choosing between two methods of organizing his bakery. Method one will require a counter person to wait on each customer individually before they proceed to the cashier to pay for their purchases. In this system, customers will arrive at the rate of 8 per hour and can be served by the counter person at the rate of 15 per hour. The cashier will be capable of serving customers at the rate of 20 per hour. For simplification purposes, assume that the arrival rate at the cashier phase is identical to the arrival rate at the first phase and that these waiting lines can be analyzed independently and combined.
Method two will have the two employees wait on customers as they selected their pastries and also collect their money once their selections have been made. Customers still arrive at the rate of 8 per hour but now the total service time (pastry selection and payment collection)takes 5 minutes per customer. Calculate the average number of customers in the bakery and the average time spent in the bakery for both systems and make your recommendations to Gerard. Assume that service times are exponentially distributed and arrivals follow a Poisson distribution.