Instructions For the problems which require Bayesian revision, please use five decimal place accuracy. You may use either tables done by hand, or tables done in Excel, or probability trees. 1. (20 marks) A company has developed a new type of mosquito repellant. The tech- nical success is clear, but as with any new product the commercial success is risky. Because of this, they would sometimes test-market a product first, and then make a decision about national marketing after the test-market results had come in; at other times they would proceed directly to national marketing. On some occasions, they would abandon the product without even test-marketing it. The test-marketing would cost about $600,000. If successful (probability 0.4) there would be revenues of $200,000; if unsuccessful the revenues would only be $50,000. Should the test market be successful, a followup national campaign at a cost of $2,500,000 would have a 70% chance of success with a revenue of $9,000,000, otherwise it would be a failure with a revenue of $750,000. Should the test market be unsuccessful, a followup national campaign would have only a 0.2 chance of success with the same cost, and the same revenues for success and failure). A national campaign not preceded by a test campaign would have a 45% chance of success. It would cost $3,000,000, and would produce a revenue of $9,500,000 if successful, but only $875,000 otherwise. (a) Draw and solve a decision tree for the situation (using payoff nodes where ap- propriate), and state the recommendation clearly. (b) If the $3,000,000 figure in the last paragraph were changed to $4,000,000, what would be the revised recommendation