Dr. Lum teaches part-time at two different community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 7 classes per semester. For every class taught by him at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers, and for each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 24 hours per week preparing lessons and grading papers. If he earns $4,200 per class at Hilltop College and $4,400 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?

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