well, once you take in all the Revenue from sales, and subtract all the costs that went in for the product, what's leftover is the Profit.
so then, profit P(x), is simply the revenue minus costs, namely P(x) = R(x) - C(x)
[tex]R(x)=100x-2x^2\hspace{5em}C(x)=500+9x \\\\\\ P(x)=(100x-2x^2)~~ - ~~(500+9x)\implies P(x)=91x-2x^2-500 \\\\\\ \stackrel{\textit{at a production of 25 units, x =25}}{P(25) = 91(25)-2(25)^2-500}\implies P(25)=\stackrel{2275-1250-500}{525}[/tex]
