Problem 3. Consider a two-sided matching problem with 3 doctors (d1,d2,d3), and 3 programs (p1,p2,p3). Each program has capacity 1. Preferences of doctors are as follows: - p1d1p2 (this means doctor 1 prefers program 1 over program 2 over being unmatched over program 3), - p1d2p3 - p2d3p1 Preferences of programs are as follows: - d3p1d2p1d1, - d1p2d3 - d2p3d1. Find the doctors-proposing stable matching and the programs-proposing stable matching (using the two versions of the deferred acceptance algorithm). (20 points) Problem 3. Consider a two-sided matching problem with 3 doctors (d1,d2,d3), and 3 programs (p1,p2,p3). Each program has capacity 1. Preferences of doctors are as follows: - p1d1p2 (this means doctor 1 prefers program 1 over program 2 over being unmatched over program 3), - p1d2p3 - p2d3p1 Preferences of programs are as follows: - d3p1d2p1d1, - d1p2d3 - d2p3d1. Find the doctors-proposing stable matching and the programs-proposing stable matching (using the two versions of the deferred acceptance algorithm). (20 points)