Problem 2 (25 marks): A system lifetime follows the lognormal distribution with parameter {,}. The cost of a failure replacement is $250 and the cost of a scheduled replacement is $70. Under the periodic maintenance, determine the optimal maintenance interval to minimize the maintenance cost rate. The following cases are considered: Case 1: =1 and =1 Case 2: =1 and =5; and Case 3: =2 and =1