Calculate commission - Rates decrease when turnover increase It's been a long time since I attended a mathematics class. Once I was able to solve this myself, but apparently not anymore:
A company gets a commission from sales. The commission is 
10% on turnover <= 1 million, 
8% on turnover > 1 million to <= 3 millions, and
6% on turnover > 3 millions
I need an equation where the actual turnover is known, and the equation gives the earned commission.
I.'ve made a couple of attempts on equations with 3 unknowns, but I have no idea where to start.
Help very appreciated!
Best regards,
Anders
 A: Here is a way of writing your function in a standard mathematical notation,
where $c(t)$ represents the total amount of the commission earned for a turnover of $t$:
$$
c(t) = \begin{cases}
 0.1 t & t \leq 1\,000\,000 \\
100\,000 + 0.08(t - 1\,000\,000) & 1\,000\,000 < t \leq 3\,000\,000 \\
260\,000 + 0.06(t - 3\,000\,000) & t > 3\,000\,000 \\
\end{cases}
$$
I chose that form because it is close to the way the rules are expressed in the problem statement. For example, when the turnover is more than three million, the formula shows that the total commission is the amount earned on the portion of the turnover that is below three million, which is
$0.1\times 1\,000\,000 + 0.08\times 2\,000\,000 = 260\,000,$
plus $6\%$ of the portion of the turnover that is above three million.
A slightly different way to write the same function is
$$
c(t) = \begin{cases}
 0.1 t & t \leq 1\,000\,000 \\
20\,000 + 0.08 t & 1\,000\,000 < t \leq 3\,000\,000 \\
80\,000 + 0.06 t & t > 3\,000\,000 \\
\end{cases}
$$
using facts such as 
$$260\,000 + 0.06(t - 3\,000\,000)
= 260\,000 + 0.06 t - 180\,000 = 80\,000 + 0.06 t.$$
