Problem 10-7 Burrito King (a new fast-food franchise opening up nationwide) has

Question

Problem 10-7 Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9,000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 50 seconds. To help determine the amount of space needed for the line at the drive-up window a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places) Average line length cars b. What is the average number of cars in the system (both in line and at the window)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number of cars cars c. What is the expected average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Expected average time minutes References eBook & Resources Worksheet Difficulty: Challenge Problem 10-7 Learning Objective: 10-02 Analyze walting line problems.

Explanation / Answer

Service rate = Lambda = 45

Arrival rate = Mu = 50

Waiting line length = (lambda^2)/(Mu*(Mu-lambda)) = 8.10

Waiting cars in system = lambda/(Mu-lambda) = 9.0

Waiting time in system = Waiting cars in system / Lambda = 0.2 sec

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