jmc

We look for the least number of workers $n$ such that the cost is less than the revenue in a day of work. The cost of each worker is \15$perhour,whiletherevenuethatcomesfromeachworkerhiredis$\$3.10\times 5$ widgets per hour. $$\begin{array}{rl}500+8(15n)& <(8)(3.1)(5)n=124n\Rightarrow \\ 500+120n& <124n\Rightarrow \\ 500& <4n\Rightarrow \\ 125& <n.\end{array}$$The smallest integer greater than 125 is 126, so the company has to hire at least $\boxed{126}$ workers to make a profit.