2. Suppose there are two schools in an area: A and B, and eight students in an area labeled s1,,s8. The students are numbered by their test score rankings, so that s1 has the highest test scores, s2 the second highest, etc. Each school can accommodate four students. All students would prefer school A, and both schools rank the students by their test scores. (a) What is the unique stable matching of students to schools? (b) Now suppose school A decides to implement a preference program that favors students who live near the school. Students s2,s6, and s8 are 'local.' Specifically, suppose slots are allocated using a DA algorithm, and A makes sure to allocate half of its slots to local students. What is the resulting match? (c) Suppose instead A divides itself into two schools A and A, each with two seats. A prioritizes by test score and A ranks by local/ not-local and within those categories by test score. What happens in the DA algorithm if students prefer A to A ? 2. Suppose there are two schools in an area: A and B, and eight students in an area labeled s1,,s8. The students are numbered by their test score rankings, so that s1 has the highest test scores, s2 the second highest, etc. Each school can accommodate four students. All students would prefer school A, and both schools rank the students by their test scores. (a) What is the unique stable matching of students to schools? (b) Now suppose school A decides to implement a preference program that favors students who live near the school. Students s2,s6, and s8 are 'local.' Specifically, suppose slots are allocated using a DA algorithm, and A makes sure to allocate half of its slots to local students. What is the resulting match? (c) Suppose instead A divides itself into two schools A and A, each with two seats. A prioritizes by test score and A ranks by local/ not-local and within those categories by test score. What happens in the DA algorithm if students prefer A to A