A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout on an average of one every 8 minutes (lets assume exponential interarrival times). The cashier takes an average of 6 minutes (lets also assume the service time has exponential distribution)to process a single customer. We assume that the service time is randomly distributed, and the customers arrive randomly. The store's owner believes that the amount of time that a customer has to wait hurts his business; he estimates that waiting time costs him $20 per customer-hour in lost business (i. e. Let's say 3 customers wait for one hour, the store incurs a cost of $20*3*1 = $60). In order to speed up service, the owner is considering hiring a teenager to bag the groceries at $6 per hour. With the addition of the bagger, the cashier will be able to process a customer in an average of 4.5 minutes. Should the bagger be hired?

Q1) Use queueing theory formulations to consult the store owner. Show your work in terms of formulas utilized, computations and discussion of results.