A burger joint has on average 9 customers arriving per hour. There is only one employee serving customers and she takes about 4 minutes on average to serve a customer. The burger joint is open 10 hours per day and makes a profit of $10 for each burger sold. The staff has a pay rate of $20/hour. Assume a Poisson distribution on the arrival rate of customers and exponential distribution on the service time of the employee.

Q. Burger joint management wants to get an automatic machine that can perform full service for customers with the same service time (4 minutes under normal distribution). If the existing employee has to match the customers average waiting time achieved by the automatic machine, how quickly would the employee have to serve each customer?