3. (20 marks) A company has identified a potential new type of cereal which would require $900,000 in start-up costs to launch. If it turns out to be a major success, there will be a $5,000,000 contribution to profit. A minor success would give a profit contribution of $1,000,000, while a failure would have a profit contribution of only $250,000. The company is most worried about this third possibility, since in this case the net profit would be $250,000 minus $900,000, i.e. a loss of $650,000. In the past, one new product in twenty became a major success, one new product in five became a minor success, and the other three-quarters of them became failures; there is no reason to suspect that this product would be any different from the rest. Some of their competitors use an outside independent market research firm to give them advice about new products. The fee for the research firm is $25,000; in return, the consumer products company would be told that the proposed product either "looks well" or "looks poorly". The research company had established a track record which gave them confidence about saying the following: (a) If a product would be a major success, they would say "looks well" with prob- ability 0.8; (b) If a product would be a minor success, they would say "looks poorly" with probability 0.7; (c) If a product would be a failure, they would say "looks poorly" with probability 0.9. Develop a decision tree and solve it to obtain a recommendation.