jmc

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 $$\begin{array}{rl}0& =-265x+2800\\ \Rightarrow -2800& =-265x\\ \Rightarrow \frac{2800}{265}& =x.\end{array}$$ 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.