Question

A food-truck has one cashier and one cook. Customers first wait in line to ‘place the order and pay the cashier’, and then enter a ‘pick-up’ line to get the food that is being prepared by the cook. Currently, the cashier can take an order and handle the money transaction in an average of 1 minutes. The cook can prepare an order in exactly 2 minutes. During an hour, 15 customers arrive on average. The interarrival times are exponentially distributed.

a) What is the average length of the “place order and pay the cashier” line? What is the average length of the “pick-up” line?

b) Whatistheaveragenumberofcustomersinthefood-truck?

c) The food-truck owner feels that the cook is slowing down the process and sends him to a training class. After the class, the cook can cook an order in exactly 1.6 minutes. What is the capacity of the system now?

d) Afterthetraining,whatistheaveragelengthofthe“placeorderandpaythecashier” line?

e) Based only in this information, would it make sense to hire another cook? Explain.

Answer 1

Part A

As per the given information, Cashier can take an order and handle the money transaction in an average of 1 minute. Therefore he can service 60 customer per hour. The service rate of Cashier is 60 customer in a hour.

Same, The cook can prepare an order exactly in 2 minutes therefore he can service 30 customer in a hour. The service rate of Cook is 30 customer.

Part B

Average no pf customers in food truck is 15 during an hour as per given informtion.

Part C

After the training, the cook can order in exactly 1.6 minutes therefore he can service 37.5 customers per hour.

The ca[acity of system now is 37.5 customers.