2. (20%) A marketing manager is considering three alternative selling strategies. The payoff table is as follows: Market demand Low (SI) Normal ($2) High ($3) Strategy I -$ 100,000 $50,000 $150,000 Strategy 2 $0 $30,000 $50,000 Strategy 3 $100,000 $20,000 $40,000 The manufacturer estimates that the probability of the market demand being Low, Normal and High are 0.3. 0.3 and 0.4 respectively. For a consulting fee of $5,000, an agency suggests to provide a research on the market demand. Suppose that the agency's research will give a result of an unfavorable market condition (I1), a normal market condition (12) or a favorable market condition (13). The conditional probabilities that summarizing the agency's accuracy are as follows: P(II | S1)=0.7, P(II | $2)=0.3, P(II | $3)=0.2; P(12 | S1)=0.2, P(12 | $2)=0.4, P(12 | $3)=0.2; P(13 | $1)=0.1, P(13 | $2)=0.3, P(13 | $3)=0.6. By constructing a decision tree, determine whether the manufacturer should hire the agency or not