A professor gives two types of quizzes, objective and recall. He is planning to give at least 16 quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a recall quiz 30 minutes. The professor would like a student to spend at least 4.5 hours (270 minutes) preparing for these quizzes above and beyond the normal study time. The average score on an objective quiz is 7, and on a recall type 5, and the professor would like the students to score at least 85 points on all quizzes. It takes the professor 2.25 minutes to grade an objective quiz, and 1.75 minutes to grade a recall type quiz. How many of each type should he give in order to minimize his grading time? a. Letting x be the first of the variables listed in the problem statement, and y the second, write the objective function. e=| b. Graph the feasible region on paper, then list the corner points of the feasible region. | ' (Enter ordered pairs (z, y), separated by commas.) c. Test the corner points to find the optimum value of the objective function: e The \"winning\" corner point is| | The optimum value of the objective function is ' |