Question

Maybe I’m overthinking this If the question is:

Rooms in a 130-unit student housing complex are fully rented

at $300 per month. The university is raising rates to produce $1920 more in monthly income from these units. Each $10 per month increase will create 2 vacancies with no possibility of filling them. What should be charged for the new rent?

I know how to maximize rent using the first derivative of 39000 + 700x – 20x^2 and setting it to zero. I can’t make the connection to increase the total revenue by a specific amount. What am I missing?

Math