Reference no: EM132813515

Herbie is a student at the Marshall School. Prior to meeting with his project team for his favorite class, Herbie likes to grab a quick bite. He has two favorite options: he could either go to "Seeds" or to "Little Galen". Herbie knows from his team members that Seeds receives a new customer every 4 minutes on average and on an average it takes 3 minutes for the food to be prepared. On the other hand, Little Galen receives a new customer every 3 minutes on average, and on an average it takes 2 minutes for the food to be prepared. Inter-arrival times at both restaurants are exponentially distributed, and their service times are exponentially distributed. Both restaurants can service at most one person at a time and the first arriving customer is served first (they have one cooking line and one cashier).

(a) Which restaurant has the higher utilization? (Show your work.)

(b) Herbie does not want to wait longer (waiting plus service) than 10 minutes on average at the restaurant. Which restaurant(s) allows him to achieve this average wait time of no more than 10 minutes? Which restaurant(s) allows him to achieve this average wait time of no more than 5 minutes? Please show your corresponding work/calculations to arrive at both answers. (Show your work.)

(c) What is the average number of customers at Little Galen? At Seeds? (Show your work.)