Anew engineer is evaluating whether to use a larger-diameter pipe for a water line. it will cost $600,000 more initially, but it will reduce pumping costs. the optimistic, most likely, and pessimistic projections for annual savings are $80,000, $50,000, and $7500, with respective probabilities of 25%, 45%, and 30%. the interest rate is 8%, and the water line should have a life of 50 years. (a) what is the pw for each estimated value? what is the expected pw? (b) compute the expected annual savings and expected pw. (c) do the answers for the expected pw match? why or why not?