Q.1. Monica Britt is considering the possibility of starting a company to produce small sail boats for the recreational market. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With favorable market, Monica can expect to make $100,000 from a large facility, or $60,000 for a smaller facility. If the market is unfavorable, however, Monica estimates that she would lose $40,000 with a large facility, and she would lose only $15,000 with the small facility. Building no facility at all yields no loos nor gains. Because of the risks involved, Monica decided to conduct a market study to assess situation for future demand for the sailboats. She estimates that the market study will cost her $1,500. Furthermore, the market study is an imperfect information tool. The market study can determine good market conditions 80% of the time whenever market conditions are good. That is P(Market study indicating good markets /markets are good)=0.80. And it can determine a bad market conditions 70% of the time whenever market conditions are bad, or P(Market study indicating bad markets/Markets are bad)=0.70. The probability of a good market condition is P(market is good)=0.65. (9 marks). a. Find the EVPI? b. Find the EVII, and discuss whether she should conduct the market survey or not? Q.2. For the stock market problem for which the decision tree is shown below. If the decision makers' utility function can be represented nicely by (6 marks) U(x) = 1.006 -0.136e 600 Where x represents the net profit High-Risk Stock (0.5) (0.3) 1900 100 (0.2) 10,89 10, 285 1000 (0.5) (0.3) 1100 300 0984 Low-Risk Stock 10,923 (0.2) -200 0,816 Savings Account 350 0,930 a. Estimate the expected monetary value and the solution path b. Based on the utility function given, determine the decisions makers expected utility and the associated solution path. Approximate utility figures for two significant digits only. c. Determine his Certainty equivalent for each alternative, which alternative should be selected, d. Do you see any difference between b and c Hint:- Utility values may exceed 1.0 Q.1. Monica Britt is considering the possibility of starting a company to produce small sail boats for the recreational market. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With favorable market, Monica can expect to make $100,000 from a large facility, or $60,000 for a smaller facility. If the market is unfavorable, however, Monica estimates that she would lose $40,000 with a large facility, and she would lose only $15,000 with the small facility. Building no facility at all yields no loos nor gains. Because of the risks involved, Monica decided to conduct a market study to assess situation for future demand for the sailboats. She estimates that the market study will cost her $1,500. Furthermore, the market study is an imperfect information tool. The market study can determine good market conditions 80% of the time whenever market conditions are good. That is P(Market study indicating good markets /markets are good)=0.80. And it can determine a bad market conditions 70% of the time whenever market conditions are bad, or P(Market study indicating bad markets/Markets are bad)=0.70. The probability of a good market condition is P(market is good)=0.65. (9 marks). a. Find the EVPI? b. Find the EVII, and discuss whether she should conduct the market survey or not? Q.2. For the stock market problem for which the decision tree is shown below. If the decision makers' utility function can be represented nicely by (6 marks) U(x) = 1.006 -0.136e 600 Where x represents the net profit High-Risk Stock (0.5) (0.3) 1900 100 (0.2) 10,89 10, 285 1000 (0.5) (0.3) 1100 300 0984 Low-Risk Stock 10,923 (0.2) -200 0,816 Savings Account 350 0,930 a. Estimate the expected monetary value and the solution path b. Based on the utility function given, determine the decisions makers expected utility and the associated solution path. Approximate utility figures for two significant digits only. c. Determine his Certainty equivalent for each alternative, which alternative should be selected, d. Do you see any difference between b and c Hint:- Utility values may exceed 1.0