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?
highest state appropriations to higher education in fiscal year 2011 per resident refers to MAX(state_appr_value); lowest number of undergraduates refers to MIN(student_count); in 2010 refers to year = 2010;
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