A company is trying to decide what to do in the incoming year to maximize profit. It could either invest in building a new product or strengthen the products it has right now. If it decides to build a new product, then it could choose to develop the product either rapidly or thoroughly. The cost of developing a product rapidly is $120,000, and the cost of developing a product thoroughly is $300,000. If the company develops the product rapidly, then the market will react well with probability 0.1, the market will react moderately with probability 0.3, and the market will react poorly with probability 0.6. If the company develops the product thoroughly, then the market will react well with probability 0.4, the market will react moderately with probability 0.4, and the market will react poorly with probability 0.2. The anticipated profit for this new product when the market reacts well, moderately, and poorly is $800,000, $200,000, and $80,000, respectively. If the company decides to strengthen its existing products, the cost is $100,000, and the market will react well, moderately, and poorly with probabilities 0.3, 0.5, and 0.2, respectively. The anticipated profit for the existing products when the market reacts well, moderately, and poorly is $400,000, $100,000, and $60,000, respectively.

(a) (25 pts) Draw the decision tree, label the nodes with letters and classify them by their types, include the outcomes with probabilities as well.

(b) (15 pts) Calculate the expected payoff of each choice, what is the optimal strategy?