Deferred Acceptance: Suppose the Gale-Shapley mechanism is used to allocate medical residents to hospitals, with the residents proposing to the hospitals. Suppose the residents' preferences are b1 \succ b2 \succ b3 b1\succ b2 \succ b3 b1 \succ b2 \succ b3 and the hospital rankings are a1 \succ a2 \succ a3 a1 \succ a2 \succ a3 a1 \succ a2\succ a3 (a) Determine the final allocation of residents to hospitals. (b) Is this the optimal stable match for residents? For hospitals? Explain