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 $5,000 per class at Hilltop College and $4,600 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income? a. Letting a be the first of the variables listed in the problem statement, and y the second, write the objective function. x= b. Graph the feasible region on paper, then list the corner points of the feasible region. (Enter ordered pairs (x, y), separated by commas.) c. Test the corner points to find the optimum value of the objective function: The "winning" corner point is . The optimum value of the objective function is