The Capital Tour Company offers five-day tours of Ottawa for groups of students. Some of the company's costs per student go down as the number of students increases. Other costs go up because of room rentals, meals, and the number of vans that are needed. To determine the profit per student, p dollars, the company uses the function p = -0.6n^2 + 36n - 440, where n represents the number of students taking a tour.
a) Determine the maximum profit per student and the number of students that give the maximum profit per student.