The revenue \( R \) for selling \( x \) mountain bikes is \( R=248.55 x \). The cost to produce \( x \) bikes is \( C=52,000+130 x \). Find the number of bikes that the company needs to sell to produce a profit. (Hint: A profit occurs when revenue exceeds cost.) At least bikes need to be sold to produce a profit.

To find the number of mountain bikes that need to be sold to produce a profit, we need to determine when revenue \( R \) exceeds cost \( C \). The revenue is given by: \[ R = 248.55 x \] The cost is given by: \[ C = 52,000 + 130 x \] We want to find when \( R > C \): \[ 248.55 x > 52,000 + 130 x \] Rearranging this inequality gives: \[ 248.55 x - 130 x > 52,000 \] \[ 118.55 x > 52,000 \] Now divide both sides by 118.55: \[ x > \frac{52,000}{118.55} \approx 438.12 \] Since \( x \) must be a whole number, the company needs to sell at least 439 bikes to produce a profit. So, at least **439** bikes need to be sold to produce a profit.