Princeton has an endowment of 5 million dollars and wants to invest it into improving campus life. The university has three options: it can either invest in improving the dorms, campus parties or dining hall food quality. If they invest a million dollars in the dorms, the students will spend an additional 5 a hours per week studying. If the university invests b million dollars in better food, the students will spend an additional 3 b hours per week studying. Finally, if the c million dollars are invested in parties, students will be more relaxed and spend 11 c-c^{2} more hours per week studying. The university wants to invest its 5 million dollars so that the students get as many additional hours of studying as possible. What is the maximal amount that students get to study?