A firm must sell a large quantity of cement either today or tomorrow. Today's price is 145$ per unit. The firm believes that tomorrow's price could be either 100$ or 200$ per unit. Letting X represent tomorrow's price, the prior probabilities are: Pr(X=100$) = 0.3, Pr(X=200$) = 0.7. a) What is the optimal alternative? b) What is the expected value of perfect information? c) A market expert offers to give his prediction on tomorrow's price. That is, he will say to the firm: "In my opinion, tomorrow's price will be x, where x will be either 100$ or 200$. The firm knows that the market expert is right 60% of the time. For his service, he charges a commission, which is equal to 1.5$ per unit of cement sold. Draw the corresponding decision tree and decide whether the firm should employ the market expert or not.