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I'm trying to figure out how to make a formula to solve this problem:

Say that you get paid commission based on how much you sell. If you sell anywhere from \$0 to \$5000, you get a commission rate of 8%. If you sell anywhere from \$5000.01 to \$10,000, you get a rate of 10%. Anything above \$10,000 gets a rate of 12%.

The trick comes with how the interest is applied. For example, if you sold $15,000:

the first $5000 gets %8
the second $5000 gets %10
and the third $5000 would get %12

resulting in

(5000 * 0.08) + (5000 * 0.10) + (5000 * 0.12) = 1500

Is there a way to create a formula for this? Also, I tagged this as linear algebra as I figure the formula will be algebraic, but I don't actually know what to tag this as.

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up vote 1 down vote accepted

$x = $ Total Sold

Profit Earned $= \min(x,5000)*0.08+\max(\min((x -5000),5000),0)*0.1+\max((x-10000),0)*0.12$

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thanks so much! – LordZardeck Oct 17 '12 at 19:43

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