The profit (in R1000s) yielded by a company, using a machine that produces bottle caps, is dependent on the average speed at which the machine runs.
The profit (P) is calculated using the formula:
where $v$ is the average speed (in kilometers per hour) and $v>0$
- Calculate the average speed at which neither a profit , nor a loss is yielded.
- Determine at what average speed the machine should run so that the maximum profit is obtained.
- Hence, or otherwise, calculate the resulting maximum profit.