1. James has unintentionally insulted a competitor, Greg, on social media. They must now duel. However, they live far away from each other, in two different cities. To be fair to both parties, they decide to meet at an intermediate city. So, they each start driving towards each other. Where should they meet? Suppose there is a set of C cities, and it takes t(x, y) time to travel between two citiesx, y E C. James is located at city a, and Greg is located at city b. Describe and analyze an algorithm that finds the best city x for the two to meet such that they meet up as quickly as possible. 2. Dayton is planning a trip to the country "Fraela". USD is not accepted in Fraela. Instead, you need FDM- the Fraelan currency. Dayton has a list of all currencies in the world and the exchange rates between all of them. Note that exchange rates may not be symmetric (ex. just because you can exchange 8 USD for 2 Euro does not mean you can exchange 2 Euro for 8 USD). You can assume that the exchange rate does not depend on how much money you are exchanging. Describe and analyze an algorithm to find the best sequence of exchanges to FDM so that you end up with the most amount of FDM at the end.