3. (Class 5) [30 points] A soft drink company is considering launching a 'seasonal soda' that will be sold for a limited duration. They are considering selling the new soda X-Mist during the upcoming summer season. The company believes, based on its limited market analysis, that there is a 0.75 probability that X-Mist will have a successful summer season and have 2 estimated that they will receive a profit of $4 million if it is successful. If X-Mist is not successful over the summer season, the company will incur a loss of $900,000. The firm Market-Strategies can do an extensive market analysis for a fee of $35,000. MarketStrategies has demonstrated that it is 90 percent reliable in its market analysis for soft drinks, i.e., a soda that will be successful in the market will be reported as 'Successful' by MarketStrategies with a probability 0.9 and a soda that will not be successful in the market will be reported as 'Fail' by Market-Strategies with a probability of 0.9 . The soft drink company must decide whether to launch X-Mist and whether to hire MarketStrategies to conduct this market analysis prior to making the launch decision on X-Mist. (a) (10 points) Construct the decision tree for this problem which includes the decisions of whether or not to hire the firm and whether or not to launch the soda. (b) (5 points) Find the probabilities for the branches emanating from the chance nodes. Please provide all 'intermediate probabilities' (i.e., probabilities you calculated but do not appear in the branches) you used to determine the probabilities relevant to the problem. (c) (10 points) Analyze the decision tree to identify the optimal policy. Please provide for each chance node the expected payoff and for each event node the payoff of that node based on the best decision. (d) (5 points) Now suppose that Market-Strategies fee is negotiable. What is the maximum amount that the soft drink company should pay them