4. The consulting firm Advice Experts LLP strives to put project teams together by mutual agreement between the partner who leads the team and the analyst who joins it. Currently, there are three projects (A, B, and C), and three available analysts: Juan, Rahul, and Yee. The partners all prefer the analysts in that order, and each project only requires one analyst. The analysts' preferences are as follows: 1st 2nd 3rd Juan B C A Rahul Yee A B A B (i) What is the matching using the Deferred Acceptance Algorithm with partners proposing (assuming that analysts are sincere)? (ii) What is the matching when analysts propose instead? (iii) What is the matching when partners propose, and the Partner who leads B prefers Yee to both Juan and Rahul instead? (iv) What is the matching when analysts propose, and the Partner who leads B prefers Yee to both Juan and Rahul? 5. Based on Problem 4, with partners all preferring Juan to Rahul, and Rahul to Yee: (i) Suppose a new project D was just created, and the partner who leads it prefers the analysts in the same order as the other partners. Which analyst 3 preferences would result in Juan working for D (assuming partners propose, and everyone acts according to the algorithm)? (ii) If D instead prefers Yee to Rahul to Juan, what is an example of analyst preferences that would result in Juan working for D? (iii) A new analyst, Noor, has just started to work for Advice Experts. She has the same preferences as Juan, but because she is still unknown all the partners rank her lowest. Using your analyst preferences from (iv), with partners proposing and truthfulness among analysts, which project will Noor be assigned to?