Dirigible’s Burgers is a highly popular burger restaurant in Ithaca. Their busiest period is the lunch rush from 11am to 2pm, during which an average of 300 customers arrive. Interarrival times are exponentially distributed. Customers wait in a single line and give their orders directly to the kitchen before paying the cashier. The kitchen at Dirigible’s has two grill cooks (each of whom can cook one burger at a time), and each cook can produce 60 burgers per hour. Because Dirigible’s offers a wide variety of choices for burgers, the cooking time is highly variable, with a standard deviation of 1.5 minutes.
a) On average, how long does it take each customer to receive her burger from the kitchen since when she enters the restaurant?
b) What is the average number of customers waiting in line (not including the ones that are being served right now)?
c) If Dirigible’s wants to reduce the average time a customer spends before receiving the burger to at most two minutes, how many more cooks do they need?