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Question 3 (2 points): A single high-speed pump at an industrial water treatment facility operates on an emergency basis to prevent releases of untreated wastewater when severe rainfall events occur, by diverting excess water volumes to protected overflow ponds. The cost to the operator of untreated wastewater spills to the environment has an unknown value, $X. The pump has a Weibull distributed time to failure, with a characteristic life of 500 hours, and a shape factor of 4.2. The pump is expected to operate for approximately 200 hours annually. Assuming replacement of the pump costs $15,000, regardless of whether it occurs on a scheduled basis or from a failure, what is the economically optimal replacement interval (by accumulated operational hours) for this pump under different assumed costs for environmental wastewater spills (from $50,000 to $500,000)?

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