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Repairs are need on the outlet works of a small dam. For a particular 36-inch gate value, there are three available alternatives: (1) leave the

Repairs are need on the outlet works of a small dam. For a particular 36-inch gate value, there are three available alternatives: (1) leave the valve as it is; (2) repair the valve; or (3) replace the valve. If the valve is let as it is, the probability the valve seats fail during the life of the dam is 0.49; the probability the valve stem fails is 0.38; the probability the valve body fails is 0.03; and the probability nothing in the valve fails is 0.1. If the valve is repaired, the probability the valve seats fail is 0.44; the probability the valve stem fails is 0.27; the probability the valve body fails is 0.12; and the probability nothing in the valve fails is 0.17. If the valve is replaced, the probability the valve seats fail is 0.2; the probability the valve stem fails is 0.21; the probability the valve body fails is 0.08; and the probability nothing in the valve fails is 0.51. The cost of future repairs and service disruption of a failure of the valve seats is $25,000; the cost of a failure of the valve stem is $48,000; and the cost of a failure of the valve body is $38,000. The cost to repair the valve now is $2200, and the cost to replace the valve now is $17,000. If the criterion is to minimze expected costs, enter the expected cost of the best alternative. You do not need to consider interest rates for this problem.

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