4. Decision Trees (40 points). Assume that you have a client that is a paper manufacturer and they have expressed concern that the government will pass a new regulation banning the use of chlorine-based technologies within their manufacturing process. If the firm were certain that the regulation would pass they would take proactive remedial action now (at a cost of $500K) and introduce a newer, compliant technology. They don't want to spend the $500K if they don't have to. If they don't act now, believing that the government will not change the regulation, and end up being wrong then they will find themselves changing their manufacturing process from a reactive position and the cost for getting in compliance will be $850K, much greater than the $500K. Currently, the company's best guess that the government will pass the new regulation is 20%. As a consultant in this area your first instinct is to see if you can get more information on the likelihood of the government moving forward and making a change. Some research informs you that there are two firms available with expertise in forecasting regulatory policy as it relates to the papermaking industry. Firm A charges $80K for a study and their record is perfect. In the past, whenever Firm A has predicted that the government would introduce a more stringent regulation the prediction always came true and for those times that Firm A predicted that no new regulation would occur, none has occurred. If Firm A were to predict a change then your client would immediately undertake proactive remedial action and if Firm A predicted no change they would maintain the current manufacturing process. Another firm, Firm B, has a much lower fee, charging only $20K but their predictive performance has not been perfect. In the past, Firm B has predicted government policy for passing new regulations with a ninety percent accuracy (i.e. for those times the government introduced a tougher