December
1998 QUESTION 4 Total Marks: 20 Marks |
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| (a) | The personnel manager of the Acme
Machine shop needs to hire a machine to fix certain type of copier when it is in need of
repair. Breakdowns on the copiers are Poisson-distributed and occur at an average of 3 per
hour. Any copier out of service, either being repaired or waiting to be repaired, costs
the company $80 per hour. The personnel manager can consider hiring either one of two applicants. The first applicant is a very speedy worker who can repair this type of copier at an average rate of 5 per hour (exponentially distributed) and expected to be paid $18 per hour. The second applicant is somewhat slower, performing an average 4 repairs per hour (also exponentially distributed service times) and he expects a wage of $10 per hour. Should the company hire either or both workers in order to minimise total cost? Assume that if both are hired, they would work as a team with mean service rate equal to the sum of two individual service rates.
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[13] |
| (b) | State seven characteristics of a simple queue. | [7] |