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Subject:Operations ManagementPrice:2.87 Bought7
Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun’s vaccination (service) times are negative exponentially distributed. Compute the following
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The probability that Tarun is idle. [ Select ] [".12", ".35", ".5", ".25"]
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The average number of dogs being vaccinated and waiting to be vaccinated. [ Select ] ["7", "4", "1", "2"]
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The average time a dog waits before getting vaccinated. [ Select ] [".15", "4.7", "3", "4"] minutes
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The average amount of time a dog spends waiting in line and being vaccinated. [ Select ] ["1.2", "6", "10", "3"] minutes
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Answer:
arrival rate=L=1 per 6 min = 1/6 per min=0.167 dog per min
Service rate=m= 1 per 3 min= 1/3 per min =0.33 dog per min
Hence L/m=0.167/0.33=0.50
a) The probability that Tarun is idle.= 1- (L/m)=1-0.50=0.5
b) The average number of dogs being vaccinated and waiting to be vaccinated=Lq+L/m=L^2/(m*(m-L) +L/m=0.167^2/(0.33*(0.33-0.167))+0.506=0.027 / 0.054 + 0.50 = 1.00 = 1
c) The average time a dog waits before getting vaccinated.=Lq/L = 0.5 / 0.167 = 2.99 = 3
d) The average amount of time a dog spends waiting in line and being vaccinated= Lq/L +1/m
= 3 + (1/0.33) = 6.03 = 6
