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 $5a$ hours per week studying. 
- If the university invests $b$ million dollars in better food, the students will spend an additional $3b$ hours per week studying. 
- Finally, if the $c$ million dollars are invested in parties, students will be more relaxed and spend $11c - c^2$ 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?

Let's think step by step and output the final answer within \boxed{}.
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