The point at which the company goes bankrupt is where $ y=0 $, the $ x $-intercept. To solve for the $ x $-intercept, we set $ y=0 $ and get \begin{align*} 0 &=-265x+2800\\ \Rightarrow\qquad -2800&=-265x\\ \Rightarrow\qquad \frac{2800}{265} &= x.\end{align*} Realizing that $ \frac{2800}{265} $ is between 10, or $ \frac{2650}{265} $, and 11, or $ \frac{2915}{265} $, then the company can hire at most $ \boxed{10} $ workers, since hiring 11 would bring it past the $ x $-intercept and into debt.