Problem 5: Network Optimization A state department of transportation is considering building a High Speed Rail system. There is uncertainty about what the future demand will be. It is believed that the high demand scenario has a probability of 60% and the low demand scenario has a probability of 40%. The net present values (NPV), in billions, under these two scenarios are given by: High Demand 100 Low Demand -50 Build High Speed Rail Do Nothing 0 0 A consultant proposes a demand study. Based on their track record, the probability that they will correctly forecast the demand scenario is 0.8. In other words: P(FH|H) = P(FLL) = 0.8 and P(FL|H) = P(FH|L) = 0.2 Where L and H are the high and low demand scenarios, and FH and FL are the consultant forecasts of high and low demand scenarios. a. If there state department of transportation decides not to fund the study, which alternative, Build High Speed Rail or Do Nothing, should it choose it choose based on expected net present value? b. If the state decides to fund the study, and the study predicts high demand, which alternative should it choose? c. If the state decides to fund the study, and the study predicts low demand, which alternative should it choose