Question

A repairman is to be hired to repair machines which break down at an
average rate of 3 per hour. The breakdowns follow Poisson distribution.
Non-productive time of machine is considered to cost Rs. 16 per hour.
Two repairmen have been interviewed: one is slow but cheap, while the
other is fast but expensive. The slow repairman charges Rs. 8 per hour
and he service broken-down machines at the rate of 4 per hour. The fast
repairman demands Rs. 10 per hour and he service at an average rate of
6 per hour. Which repairman should be hired? Assume an 8-hour
working day

Answer 1

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Answer 2

Given :- A repairman is to be hired to repair machines which break down at an average rate of 3 per hour. The breakdowns follow Poisson distribution. Non-productive time of machine is considered to cost Rs. 16 per hour.

Two repairmen have been interviewed: one is slow but cheap, while the other is fast but expensive. The slow repairman charges Rs. 8 per hour and he service broken-down machines at the rate of 4 per hour. The fast

repairman demands Rs. 10 per hour and he service at an average rate of 6 per hour. Which repairman should be hired ? Assume an 8-hour working day ?

Solution :-

Case 1) :- Slow Repairman

→ Total cost of hiring slow repairman for 8 hours = (No. of Breakdown / hour) * 8 hours * Average time spent * Breakdown cost + (Labour cost / hour) * 8 hours.

we have ,

• No. of Breakdown / hour = 3
• Average time spent = 1/(4 - 3) = 1 .
• Breakdown cost = Rs.16
• Labour cost = Rs.8 / hour

Putting all values we get,

→ Total cost of slow repairman for 8 hours = 3 * 8 * 1 * 16 + 8 * 8 = 384 + 64 = Rs.448

Case 2) :- fast Repairman

→ Total cost of hiring fast repairman for 8 hours = (No. of Breakdown / hour) * 8 hours * Average time spent * Breakdown cost + (Labour cost / hour) * 8 hours.

we have ,

• No. of Breakdown / hour = 3
• Average time spent = 1/(6 - 3) = (1/3) .
• Breakdown cost = Rs.16
• Labour cost = Rs.10 / hour

Putting all values we get,

→ Total cost of fast repairman for 8 hours = 3 * 8 * (1/3) * 16 + 10 * 8 = 128 + 80 = Rs.208

Since, the total cost of hiring the fast repairman is less, we should hire the fast repainman.

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