How much per bearing can RBI afford to spend on inspection costs before it begins to lose money on inspection?

The marketing manager of Roller Bearings International (RBI) estimates that “defective bearings that get into the hands of industrial users cost RBI an average of Rs. 200 each” in replacement costs and lost business. The production manager counters that “the bearings are only about 2 per cent defective now, and the best a sampling plan could do would be to reduce that to 1 per cent defective – but not much better (unless we go to 100 percent inspection).” Should RBI adopt a sampling plan if it costs?
i) Rs. 100 per bearing?
ii) Rs. 250 per bearing?
iii) How much per bearing can RBI afford to spend on inspection costs before it begins to lose money on inspection?


Solution. Let y be the cost of production each bearing and 1000 bearing are produced.
Production cost = 1000y
2% defective = 20 bearings
Cost of replacement and lost business = Rs. 200 each
= 200 x 20 = 4000
= Total cost = 1000y + 4000 …… (1)

If defects are reduced to 1%
Defective bearings would be 10 only

Cost of replacement and lost business = Rs. 200 x 10 = 2000

Part (i)
Revised production cost is (y + 100)
Total cost = 1000 (y + 100) + 2000
= 1000y + 100000 + 2000
= 1000y + 102000 …. (2)

Savings : Equation (1 – 2)
(1000y + 4000) – (1000y + 102000)
= 1000y + 4000 – 1000y – 102000
= - 98000 Rs.
So RBI should no adopt the sampling plan because it is losing money.

Part (ii)
RBI is losing money if the sampling plan cost is Rs. 100 per bearing. If the cost is Rs. 250 then it will lose more money. So it should not adopt the plan.

Part (iii)
Let RBI can afford Rs. z on inspection for each bearing.
Cost of inspection for 1000 bearings = 1000z
= 1000y + 1000z ….(3)

Equating equations (1 and 2)
1000y + 4000 = 1000y + 1000z
1000z = 4000
z = 4000/1000
z = 4 Rs. only
If the inspection cost is more than Rs. 4 per bearing then RBI will start losing money.