Suppose 50 people come to a fast food take-out restaurant each hour. There are four employees, one at the register, two making the food, and one packaging the food. Suppose on average, each order takes 30 seconds at the register, and it takes one employee an average of 1.5 minutes to make the food, and it takes 1 minute on average to package the food. Assume exponential arrivals and service times. How many people on average are waiting in line to place an order?

Question

Business

Camilla George

25 March, 21:11

Suppose 50 people come to a fast food take-out restaurant each hour. There are four employees, one at the register, two making the food, and one packaging the food. Suppose on average, each order takes 30 seconds at the register, and it takes one employee an average of 1.5 minutes to make the food, and it takes 1 minute on average to package the food. Assume exponential arrivals and service times. How many people on average are waiting in line to place an order?

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Tamara Hughes · Answer 1

- 50 people / 60 min = 0.833 people per minute

- Register = 60min per hour / 30 sec Per hour = 120 orders per hour.

- Making the food = 60 min / 1.5 min = 40 orders x 2 employes = 80 orders per hour

- Paking the food = 60 min / 1 min per food = 60 orders per hour

- Complete service = 30 sec + 1.5 min/2 + 1 min = 2.25 min = 26 orders per hour

- 24 people will stay in line