Answer Part B Please. Part A. Andrew Jones, the mechanic at Tivoli Muffler Shop,

Question

Answer Part B Please.

Part A. Andrew Jones, the mechanic at Tivoli Muffler Shop, is able to install new mufflers at an average rate of 3 per hour (or about 1 every 20 minutes), according to an Exponential distribution. Customers seeking this service arrive at the shop on the average of 2 per hour, following a Poisson distribution and are served on a first-in, first-out basis. Using the above data,

find - Average number of persons (units) in the system

Average time a person (unit) spends in the system

Average number of persons (units) in the queue

Average time a person (unit) spends in the queue Utilization factor for the system Probability of zero persons (units) in the system Probability of 2 persons (units) in the system

Part B. The owner of Tivoli Muffler Shop estimates that the cost of customer waiting time, in terms of customer dissatisfaction and lost goodwill, is $10 per hour of time spent waiting in line. The average car has a 2/3 hour long wait (Wq) and there are approximately 16 cars serviced per day ( i.e. 2 arrivals per hour for 8 working hours per day).

Find a) the total number of hours that customers spend waiting each day for mufflers to be installed,

and b) the total cost to the business for this wait.

Part C. The Tivoli Muffler Shop has decided to open a second garage bay and hire a second mechanic to handle installations. Customers, who arrive at the rate of about = 2 per hour, will wait in a single line until one of the two mechanics is free. Each mechanic installs mufflers at the rate of about µ = 3 per hour.

For this two-channel system, find the values for P0, Ls, Ws, Lq and Wq and then draw up a table which will compare these values with the old single-channel waiting-line system.

Explanation / Answer

a. From information given, Wq=2/3=lambda/{mu(mu-lambda)}, and L=lambda/(mu-lambda)=16

Therefore, total number of hours that customers spend waiting each day:Wq*L=2/3*16=10.67 (ans)

b. The total cost: $10*10.67=$106.7 (ans)

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