Assignment:
Tires that fail in service result in significantly higher replacement costs than those replaced before failure. For an 18-wheeler (that is, a truck with 18 tires), failure on the road costs $300, whereas all 18 tires can be replaced prior to failure at a cost of $75 per tire. The probability of failure is given in the following table.
|
Number of Miles
|
Probability of Failure
|
|
0-5,000
|
.05
|
|
5,001-10,000
|
.15
|
|
10,001-15,000
|
.20
|
|
15,001-20,000
|
.40
|
|
20,001-25,000
|
.20
|
If tires are replaced at multiples of 5,000 miles only, what is the optimal age replacement policy?
Provide complete and step by step solution for the question and show calculations and use formulas.