Scenario 2: Faraday Motors (FM) is trying to determine what size of manufacturing plant to build for a new 100% electric smart car it is developing. Only two plant sizes are under consideration: large and small. The cost of constructing a large plant is $25 million and the cost of a small plant is $15 million. FM believes there is a 70% chance that the demand for this new car will be high and a 30% chance it will be low. The following table summarizes the payoffs (in millions of dollars) the company expects to receive for each factory size and demand combination (factory costs not included): Demand Factory Size High Low $175 $95 $125 $105 Large Small Before making the plant size decision, FM could conduct a survey to assess consumer sentiment about the new car. The survey results will indicate either a favorable or unfavor- able sentiment. Based on previous experience with other vehicles and with survey results of this kind, when demand was high the survey indicates a favorable sentiment 86% of the time. When demand was low, the survey indicated favorable sentiment 22% of the time. Create a decision tree for this problem taking into account the survey/no survey decision (at first, assume there is no cost to conducting the survey). You will need to use Bayes' Rule to compute some of the required probabilities. Which course of action maximizes the EMV? 6. What is the EMV for the course of action recommended by the decision tree you built? (in millions) 7. What is the survey's EVSI? (in millions) 8. What is the EVPI for this problem? (in millions) 9. What is the probability of a favorable survey? Type this answer in with four, rather than two, digits after the decimal point (rounded as usual). 10. What is P(High Demand | Unfavorable Survey)? Type this answer in with four, rather than two, digits after the decimal point (rounded as usual).