Bearing failure in the blower used in diesel engines in semi$-$tractors has been determined as occurring according to a Weibull distribution with a mean life of $150,000$km$,$with a standard deviation of $10,000$km$.$Failure in service of the bearing results in costly repairs, and in total, a failure replacement is $10$times as expensive as a preventative replacement. a$.$Determine the optimal preventative replacement interval $($or block policy$)$to minimize total cost per kilometre. b$.$What is the expected cost savings associated with your optimal policy over a replace$-$only$-$on$-$failure policy? c$.$Given that the cost of a failure replacement is $$2000,$what is the cost per kilometre associated with your optimal policy?