7. (20 points) Let's use decision analysis to optimize the hurricane evacuation decision! Suppose that Charleston, SC is under a potential threat from Hurricane James. Hurricane James is predicted to make landfall in three days, and the last opportunity to effectively evacuate Charleston is tomorrow, that is, if we do an evacuation, it needs to be done either today or tomorrow. Of course, whether or not we should evacuate depends on the hurricane forecast, which is changing constantly due to the uncertainty in hurricane's track and intensity. We assume for simplicity that the hurricane's intensity forecast is accurate, but the forecast on its landfall location is highly uncertain. According to the forecast at the moment, the probability that Hurricane James will make landfall in Charleston area is 0.3. However, this forecast will change tomorrow based on whether Hurricane James' track shifts towards north, or south, or stays the same, which happens with the following probabilities: Suppose that the probability of landfall in Charleston area increases by 0.1 if Hurricane James shifts north, decreases by 0.1 if it shifts south, and stays at the same value if it does not change direction. For example, if Hurricane James shifts towards north tomorrow, then the probability of landfall in Charleston area will be 0.3+0.1=0.4. Assume that the loss is estimated to be $30 million if Hurricane James makes landfall in Charleston area and no evacuation is done, and $0 loss will incur if evacuation is done. The estimated cost for evacuation depends on the timing of evacuation: - If we evacuate Charleston today, the cost is $5 million; - If we evacuate Charleston tomorrow, the cost is $10 million; (a) Create a Decision Tree to decide what to do to minimize the total expected loss from Hurricane James. (b) Write down the optimal decision policy for evacuation and the expected loss for this optimal decision policy