A new engineer is evaluating whether to use a larger-diameter pipe for a water line. It will cost $350,000 more initially, but it will reduce pump- ing costs. The optimistic, most likely, and pes- simistic projections for annual savings are $30,000, $20,000, and $5000, with respective probabilities of 20%, 50%, and 30%. The interest rate is 6- 8%, and the water line should have a life of 40 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?