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Economic Tyre Replacement Policy Expected Cost Analysis Word Problem
Published on October 25, 2026
Word-Problem
A fleet maintenance word problem comparing the expected cost of replacing class C tyres now at USD 800 versus keeping them with an 80 percent road failure chance at USD 1000 each. The solution computes the expected cost of keeping a tyre as 0.8(1000)+0.2(800)=960, showing immediate replacement saves USD 160 per tyre.
Question
Answer
Solution
Step 1: Cost per class C tyre under each policy
- Replace now at the company shop: $800 per tyre.
- Keep for another month:
- 80% fail on the road and are replaced by the service company at $1000.
- 20% remain in class C and are replaced at the next inspection at the shop for $800.
Step 2: Expected cost of keeping a class C tyre
Step 3: Compare the policies
Replacing now saves $160 per class C tyre on average, so the change is worthwhile.
Final answer: The most economical policy is to replace all class C tyres at each monthly inspection with new or class A tyres at the company’s own shop, at $800 each. This gives an expected saving of $160 per class C tyre over keeping it, so the maintenance foreman’s argument is correct.