Please create a decision tree and show work.

United Studios holds the movie rights for a national best-seller, and as part of these rights also has the option to produce a sequel based on the same book. The studio is now in the process of developing the production schedule. It believes that shooting both movies simultaneously would allow significant cost savings, and both movies could be produced for a total budget of $530 million. If instead the movies are produced sequentially, the total expected cost will rise to $580 million. On the other hand, by waiting to produce the second movie until after the first movie is released, the studio will have much better information regarding the likely orospects for the sequel. Let's see how we can use a decision tree to analyze this situation. In the case in which the movies are produced simultaneously, the studio forecasts it will earn a total of $650 million from both movies, for a net profit of $120 million. While United's expected earnings imply that the movies are worth producing, there is significant uncertainty regarding the actual outcome. In fact, the expected total revenue of $650 million for both movies reflects two alternative outcomes. Based on the popularity of the book, United believes there is a 50% chance the first movie will be a blockbuster success, in which case the studio expects it will earn $495 million from it alone, and another $395 million for the sequel. If instead the first film is ust a moderate hit, it will only bring in $295 million, and the sequel will only be expected to earn $105 million. Suppose United has the rights to produce the first film, but has not yet purchased the sequel rights. a. How much are the sequel rights worth to United? Assume that the cost of the sequel is $295 million. b. Suppose United can purchase the sequel rights now for $25 million. Alternatively, United can pay $8 million now for the option to buy the sequel rights for $25 million in the future. Which should it choose? a. How much are the sequel rights worth to United? Assume that the cost of the sequel is $295 million. Without rights, expected profit from the first film is only $395 million - $295 million =$100 million. Therefore, sequel rights add $50 million to United's expected bayoff. b. Suppose United can purchase the sequel rights now for $25 million. Alternatively, United can pay $8 million now for the option to buy the sequel rights for $25 million in the future. Which should it choose? United can pay $25 million now, or buy the sequel rights only if Film I is a blockbuster, which has an expected cost of $8 million +0.5$25 million =$20.5 million. So, it should pay $8 million for the option