How many bidders to hire at five dollars each

You are selling an item, and every bidder you bring in offers an amount uniform between $\text{\char36}500$ and $\text{\char36}1000$, independently of the others. You sell to the highest bid, but recruiting each bidder costs you $\text{\char36}5$. If you pick the number of bidders to maximise expected net proceeds, what is that expected net amount?

$905$ dollars. The top of $n$ uniform bids on $[500,1000]$ has mean $1000-\tfrac{500}{n+1}$, so net proceeds are $f(n)=1000-\tfrac{500}{n+1}-5n$. Setting $f'(n)=\tfrac{500}{(n+1)^2}-5=0$ gives $n=9$, and $f(9)=1000-50-45=905$ (neighbouring integers do slightly worse).