QUESTION 4: Decision Analysis (24 points) a) Answer Question 1 and 2 below based on the following payoff table (6 points) State of Nature Alternative SI 52 Al 75 40 A2 0 100 Prior Probability 0.6 0.4 There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is $1, the research will accurately "predict S1" 60% of the time. When the true state of nature is $2, the research will accurately "predict $2" 80% of the time. 1. What is the expected value of perfect information? (3 points) 2. What is the posterior or revised probability of $1 given that the research predicts $1 (e.g. P(S1/ predict S1)? (3 points) b) Find the optimal decision and its expected value for the MINIMIZATION problem depicted in the following decision tree, where the numbers at the end of the tree are incurred costs. State verbally the decision strategy. (4 points) A 30 5 E - 15 C F 35 B G -20 D 5 H 30 40c) The Amber Corp. is faced with the decision as to whether or not to make a bid for producing a new motor assembly for a large automobile producer. If Amber decides to bid, this will cost them $100,000 in research and development (R&D) activities. Even with the R&D, there is only a 40% chance of winning the contract. If Amber wins the contract, they will be able to sell 10,000 motor assemblies at a price of $100 per assembly. To produce these 10,000 motor assemblies they can choose to use existing technology or new technology as detailed below: Existing technology: This will cost $80,000 for modification of the current machines; in addition, variable (per unit) production cost will be $40/unit. In addition, the current machines are not as fast as desired, and there is a chance that overtime (OT) costs will be incurred (depending on other business activity at Amber) as described in the following table: Other business Probability Overtime cost activity Heavy .2 $400.000 Medium .7 $200.000 Light SO . New technology: The cost of new technology is $520,000. Variable (per unit) cost will be only $20/unit, and there is no need for overtime since the new technology includes much faster machines. Formulate the above problem as a decision tree. (Suggestion: keep track of cash/payoff flows in units of $1,000). FORMULATE ONLY. DO NOT SOLVE for the optimal strategy. (14 points)