. Departmental policy limits the size of classes to 25 for graduate students, 35 for lecturers, and 40 for professors. The teaching cost per class is $4000 for graduate students,
$5000 for lecturers, and $10000 for professors. The department requires that the lecturers
teach at least 60% more classes than graduate students and that the professors teach at least as
many classes as the total for graduate students and lecturers. If the total finite mathematics
enrollment is 1150 students, find the number of sections taught by graduate students, lecturers,
and professors to minimize teaching costs.