The following payoff table shows prot for a decision analysis problem with two decision alternatives and three states of nature. (a) Construct a decision tree for this problem. Description Decision Tree 51 57 2 53 51 1 57 3(a) Construct a decision tree for this problem. Decision Tree Description - A decislon tree begins at decision node 1 and an upper and lower branch extend from this node to the right. The upper branch, labeled :11, stops at chance node 2 and an upper, middle and lower branch extend from this node to the right. The lower branch, labeled d2, stops at chance node 3 and an upper, middle and lower branch extend From this node to the right. - The branches extending from decision node 1 from top to bottom are labeled all and d2. The next set of branches from top to bottom are labeled s1, 52, 53, 51, s2 and 53. There is an answer blank at the end of each branch. (b) If the decision maker knows nothing about the probab ties of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? mmended decision using the optimistic approach is V . The recommended decision using the conservative approach is . 'I11e recommended decision using the minimax regret approach