QUESTION 1: (4 pts) A mechanic part used in a steam boiler follows a normal failure law with mean of 10000 hours and standard deviation of 2000 hours. The preventive maintenance team has decided to apply the "Constant Interval Replacement Policy" to this component. The cost of preventative replacement is $1000 and that of the failure replacement is $3000. Assume preventive replacement can be performed at intervals from 2000 hours to 10000 hours with 2000 hours increment, find the optimal replacement period (which yields the lowest unit time cost)! The following table provides the values for M(tp) which is the expected number of replacements during the various maintenance length tp