# Math Help - Application of Derivatives ( Optimization )

1. ## Application of Derivatives ( Optimization )

A real estate developer estimates that if 60 luxury houses are built, the average profit will be $47,500 per house. The average profit will decrease by$500 per house for each additional house built. How many houses should the developer build to maximize total profit?

I set up the equation like this:
P(x) = [47500 - 500( x - 60 )]x

I get the wrong answer though, I need to get 17 or 18.

2. Just out of curiosity - do you get the result 77.5, while the key tells you 17 or 18?

3. yep - maybe i am setting up the equation wrong?

4. To be honest, I think we're looking at more of a semantic problem here:
77.5 - 60 = 17.5

After all, the problem only defines a linear correlation for the average profit after sixty houses have been built.