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# A decision has been made

A decision has been made to perform certain repairs on the outlet works of a small dam. For a particular 36-inch gate valve, there are three available alternatives:A. Leave the valve as it is.B. Repair the valve.C. Replace the valveIf the vave is left as it is, the probability of a failure of the valve seats, over the life of the project, is 60%; the probabiity of failure of the valve stem is 50%; a,d of failure of the valve body is 40%. If the valve is repaired, the probability of a failure of the seats, over the life of the project, is 40%; of failure of the steam is 30%; and of failure of the body is 20%. If the valve is replaced, the probability of a failure of the seats, over the life of the project, is 30%; of failure of the steam is 20%; and of failure of the body is 10%. The present worth of cost of future repairs and service disruption of a failure of the seats is \$10,000; the present worth of cost of a failure of the steam is \$20,000; the present worth of a failure of the body is \$30,000. The cost of repairing the valve now is \$10,000; and of replacing it is \$20,000. If the criterion is to minimize expected costs, which alternative is best?I know the answer is to repair the valve, I need help on methods to solve the problem.