Question

The restaurant at the Art Gallery of Ontario serves a hot buffet cafeteria-style daily to visitors and employees. The buffet is self-service. From 7:00 A.M.. to 9:00 A.M., customers arrive at the buffet at a rate of eight per minute; from 9:00 A.M. to noon, at four per minute; from noon to 2:00 P.M., at 14 per minute; and from 2:00 P.M. to closing at 5:00 P.M., at eight per minute (Poisson distributed). All the customers take about the same amount of time to serve themselves and proceed to the buffet. Once a customer goes through the buffet, it takes an average of 0.4 minute (exponentially distributed) to pay the cashier. The gallery does not want a customer to have to wait longer than four minutes to pay. How many cashiers should be working at each of the four times during the day?