A newly constructed cafeteria at a large government office expects to service 800 people per day. Since most workers begin their lunch break between 12:00pm and 12:40pm, food and cashier stations must be able to process a large number of workers over a short period of time.
a) Assume that the 800 workers arrive to lunch at a uniform rate between 12:00pm and 12:40pm. If it takes 15 seconds for a cashier to process a customer, how many cashiers are needed to avoid a line?
b) Each standard cash register costs $2,000. A deluxe cash register equipped with an automatic change-issuing machine, sells for $2,500. The automatic change-issuing machine is thought to reduce processing time per customer from 15 to 12 seconds. Which type of cash register do you recommend buying?