#### Answer

At least $250$.

#### Work Step by Step

The equation according to the question, because the average daily cost must be not greater than $100$: $\overline{C}(x)\leq100\\\frac{80x+5000}{x}\leq100\\80x+5000\leq100x\\5000<20x\\250\leq x$
Hence at least $250$ bicycles must be produced.