Database: college_completion
Question: In the state with the highest state appropriations to higher education in fiscal year 2011 per resident, which institution has the lowest number of undergraduates in 2010?
SQL: SELECT T1.chronname FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 ON T2.state = T1.state INNER JOIN institution_grads AS T3 ON T3.unitid = T1.unitid WHERE T1.student_count = ( SELECT MIN(T1.student_count) FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 ON T2.state = T1.state INNER JOIN institution_grads AS T3 ON T3.unitid = T1.unitid WHERE T3.year = 2010 ) AND T3.year = 2010 GROUP BY T1.state ORDER BY SUM(T2.state_appr_value) DESC LIMIT 1