1. (a) A factory owner must determine whether he should continue to produce shirts or switch to produce face masks. If face masks are produced and the epidemic is serious, he earns $10500; if shirts are produced and the epidemic is serious, he loses $500. On the other hand, if face masks are produced and the epidemic is mild, he loss $1500; if shirts are produced and the epidemic is mild, he earns $8500. Under the current situation, it is generally believed that there is a 20% chance that the epidemic is serious and 80% is mild. Before producing, he can pay $500 for an expert to use big data to forecast if the epidemic is serious or is mild for the summer. In the past, if the epidemic is serious, there is an 85% chance the expert predicts it correctly; if the epidemic is mild, there is a 96.25% chance the expert predicts it correctly. Use a decision tree to determine the factory's optimal strategy. Also calculate EVSI and EVPI. (13 marks) (b) A company is planning to invest in four different projects. The returns will depend on a number of market factors. After a careful analysis, the following opportunity loss table can be developed: Investment Good Market ($) Fair Market ($) Poor Market ($) $0 $10,000 $5,000 Project A Project B Project C $30,000 $10,000 $0 $10,000 $0 $6,000 Project D $20,000 $5,000 $3,000 The company would like to choose one project to invest. The company makes a forecast that there is a 40% chance that the market will be Good and a 20% chance that the market will be poor. The company would like to choose one project to invest. The company makes a forecast that there is a 40% chance that the market will be Good and a 20% chance that the market will be Poor. i. Calculate the optimal EOL. ii. What is EVPI? Explain. iii. Suppose the payoff for Project A is also known as follows: Investment Good Market ($) Fair Market ($) Poor Market ($) Project A $50,000 $10,000 -$10,000 Recover the complete payoff table. iv. If he is optimistic, what would be his decision? V. If he is pessimistic, what would be his decision? (12 marks) 1. (a) A factory owner must determine whether he should continue to produce shirts or switch to produce face masks. If face masks are produced and the epidemic is serious, he earns $10500; if shirts are produced and the epidemic is serious, he loses $500. On the other hand, if face masks are produced and the epidemic is mild, he loss $1500; if shirts are produced and the epidemic is mild, he earns $8500. Under the current situation, it is generally believed that there is a 20% chance that the epidemic is serious and 80% is mild. Before producing, he can pay $500 for an expert to use big data to forecast if the epidemic is serious or is mild for the summer. In the past, if the epidemic is serious, there is an 85% chance the expert predicts it correctly; if the epidemic is mild, there is a 96.25% chance the expert predicts it correctly. Use a decision tree to determine the factory's optimal strategy. Also calculate EVSI and EVPI. (13 marks) (b) A company is planning to invest in four different projects. The returns will depend on a number of market factors. After a careful analysis, the following opportunity loss table can be developed: Investment Good Market ($) Fair Market ($) Poor Market ($) $0 $10,000 $5,000 Project A Project B Project C $30,000 $10,000 $0 $10,000 $0 $6,000 Project D $20,000 $5,000 $3,000 The company would like to choose one project to invest. The company makes a forecast that there is a 40% chance that the market will be Good and a 20% chance that the market will be poor. The company would like to choose one project to invest. The company makes a forecast that there is a 40% chance that the market will be Good and a 20% chance that the market will be Poor. i. Calculate the optimal EOL. ii. What is EVPI? Explain. iii. Suppose the payoff for Project A is also known as follows: Investment Good Market ($) Fair Market ($) Poor Market ($) Project A $50,000 $10,000 -$10,000 Recover the complete payoff table. iv. If he is optimistic, what would be his decision? V. If he is pessimistic, what would be his decision? (12 marks)