Problem 4. [12 points) Elon Mask is the CEO of a company called Space Y. He is thinking about sending an expedition mission to an asteroid hovering around Mars that is made with pure diamond. If Mr. Mask decides to send the mission, he needs to invest $100 today (i.e. t = 0). The rocket will land on the asteroid next year (i.e. t = 1). Unfortunately, the asteroid is very small and there's 50% chance that rocket lands on the dark side of the asteroid, which hampers the extractor's capability as it runs on solar power. If the rocket lands on the bright side, the extractor will collect $250 billion worth of diamond each year for 50 years, starting the year after it has landed on the asteroid. However, if the rocket lands on the dark side, it can only extract $100 billion worth of diamond each year for the next 50 years. The cost of capital for this project is 100% (Hey, space is a dangerous place). a) Should Mr. Mask pursue the project? b) Now, suppose instead of going straight to the asteroid, there is an option of landing on Mars and picking up the high-functioning generator which Astronaut Mark Watney has left behind when he left Mars hastily a few years ago. There is no direct cost for this, but this will add an additional year to the Journey (i.e. reach the asteroid at t = 2). With the generator, the extractor will collect $400 billion worth of diamond each year for the next 50 years regardless of where it lands. Should the expedition land on Mars to pick up the generator? c) Since the generator is property of NASA, Mr. Mask will need to pay for the generator if he were to pick it up from Mars. What is the maximum amount Mr. Mask would be willing to pay for the generator