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M5 Solved Problems

# M5 Solved Problems - MODULE 06 ADDITIONAL PROBLEM#1 The...

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MODULE 06: ADDITIONAL PROBLEM #1 The Burger King in the ASU-MU has only one person working at the register. Customers arrive 12 per hour according to a Poisson distribution. The Burger King employee on average can help 16 customers per hour according to an exponential distribution A. What percentage of the time is the Burger King employee busy? B. What is the average number of customers WAITING to be helped? C. What is the average waiting time for customers in line? (In minutes) D. If you plan on taking home your meal, how long would you expect to be in the Burger King? (In minutes) E. How many customers would have to be in the Burger King if you wanted 1 customer in the line? F. What is the probability there is more than one person in the Line?

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The Burger King in the ASU-MU has only one person working at the register. Customers arrive 12 per hour according to a Poisson distribution. The Burger King employee on average can help 16 customers per hour according to an exponential distribution FIND GIVENS FIRST: λ = mean arrival rate = 12customers / 1 hour μ = mean service rate = 16 customers / 1 hour MODULE 05: ADDITIONAL PROBLEM #1
The Burger King in the ASU-MU has only one person working at the register. Customers arrive 12 per hour according to a Poisson distribution. The Burger King employee on average can help 16 customers per hour according to an exponential distribution A. What percentage of the time is the Burger King employee busy? ρ = λ / μ ρ = (12/hr) / (16/hr) ρ = 0 .7 5 0 MODULE 06: ADDITIONAL PROBLEM #1 Worker is Busy 75.0% of the Time

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Avg. number of customers in queue  :  l  = ρ [ λ / ( μ - λ 29 ] l  =  0.750  [ 12 / ( 16 - 12 ) ] l  =  2.25 customers DO NOT ROUND MODULE 06: ADDITIONAL PROBLEM #1 The Burger King in the ASU-MU has only one person working at the register. Customers arrive 12 per hour according to a Poisson distribution. The Burger King employee on average can help 16 customers per hour according to an exponential distribution B. What is the average number of customers WAITING to be helped?
Avg. time in queue  :  l  = ρ [ 1 / ( μ - λ 29 ] l  =  0.750  [ 1 / ( 16 - 12 ) ] t l = 0.1875 hours * (60min/hr) t l = 11.25 minutes That’s a long wait at Burger King, isn’t it? MODULE 06: ADDITIONAL PROBLEM #1 The Burger King in the ASU-MU has only one person working at the register. Customers arrive 12 per hour according to a Poisson distribution. The Burger King employee on average can help 16 customers per hour according to an exponential distribution C. What is the average waiting time for customers in line? (In minutes)

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Avg. time in system  :  s  = 1 / ( μ - λ 29 s  =  1 / ( 16 - 12 )  t s = 0.25 hours * (60min/hr) t s = 15 minutes That’s a lengthy take-out experience.
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M5 Solved Problems - MODULE 06 ADDITIONAL PROBLEM#1 The...

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