Question 2. (50 pts) You are an adventurous traveler who has saved $7,000 for exciting opportunities. Over the next three years, you have the chance to invest your money in either of two options, Option A or Option B, each with uncertain outcomes. Let's explore the details of each investment: Option A represents a thrilling adventure sports company. This option offers two potential outcomes for each year: With a higher probability of 0.7 , the adventure sports industry booms, and your investment of $7,000 multiplies to $14,000, resulting in a profit of $7,000. However, there is also a probability of 0.3 that the industry faces a downturn, and you may lose your entire investment of $7,000. Option B represents a unique eco-tourism project. This option offers two potential outcomes for each year: With a lower probability of 0.3 , the eco-tourism sector flourishes, and your investment of $7,000 grows to $14,000, resulting in a yrofit of $7,000. Alternatively, there is a higher probability of 0.7 that the project faces challenges, and you will only receive back your initial investment of $7,000. You are allowed to make only (at most) one investment each year and you can invest only $7,000 each time. (Any additional money accumulated is left idle.) a. (25 pts) Use dynamic programming to find the investment policy that maximizes the expected amount of money you will have after 3 years. b. (25 pts) Use dynamic programming to find the investment policy that maximizes the probability that you will have at least $14,000 after 3 years