Problem 4: Decision Trees Analysis (4 points) The company you are work for considers a new research project, whose objective is to introduce a new product to the market. The potential profits seem promising, however you are concerned that the probability of the project success is only 0.5. Moreover, if the project turns out to be a success, your company will have to build a manufacturing facility. In adddtion, the future profits depend on the level of demand, which is uncertain. Another option for your company is to see the rights to produce the product. In such case, the company will choose not build the manufacturing facility. The decision tree for the problem is shown below. The picture shows the estimated profits (in mln zl) for the different scenarios. The probabilities associated with different levels of demand are shown using symbols [.]. High Demand (0.5) 25 Build a Facility Medium Demand (0.3] 15 Low Demand (0.2) 5 Success (0.51 Start a Project Sell the Rights to the Product 10 -8 Failure (0.5) Do not Start a Project 0 Analyze a decision tree for the problem and choose the optimal course of action. What is the expected payoff for the optimal decision strategy (in mln. z)? (show your computations on the picture above) (2 points) Expected payoff = Suppose that the project turned out to be a success. You are now facing a choice whether to build a manufacturing facility or to sell the rights to the produce the product (you are now at the decision point 3). What is the maximum price you would pay to obtain information about a future demand (if such information would be available) in order to make an optimal decision using this information? (Show your computations) (2 points) Expected value under certainty = . Expected value under risk = Answer =