Formulating Incremental Commission

Hi,

I'm trying to formulate the following multiplier sales commission structure:

Base Annual Salary - b

Charge Out - c

Individual's commission - i

Where c is < 1b then individual's commission is equivalent to 9% of c

where b < c < 2b then i is equivalent of 12.5% of c

where 2b < c < 3b then i is equivalent of 20% of c

where 3b < c < 4b then i is equivalent of 25% of c

where 4b < c then i is equivalent of 30% of c

As an extension to this, how would one figure out the optimum salary for any given target total annual income?

Since I'm not sure what area of maths this is (although I have a feeling it's something to do with sets) I also don't know whether I am repeating another thread.

Many thanks to anyone can help me out with this one.

R