Question 4 (2 points): A smokestack scrubber at a specialty steel manufacturer has a time to failure that is Weibull distributed with a characteristic life of 12,000 hours, and a shape factor of 1.3. Replacement of the scrubber has a cost of $20,000, whether scheduled or unscheduled, but failure during service adds an additional $10,000 in costs. Assuming the scrubber operates nearly continuously throughout the year (approximately 700 hours per month or 8,640 hours per year), calculate the costs of various mandatory replacement schedules for the scrubber, and report the optimal interval