I am working on a model to set a price that maximizes profits. The equation for profits is:
Profits=price x (# sold) - (fixed cost) x (# sold)
I have models that predict (# sold) and (fixed cost) is a constant. So my first thought is to take the derivative of Profits with regards to price and set it equal to 0:
dProfits/dprice = 0
but since profits is linear and (# sold) and (fixed cost) are basically constants in this scenario, wouldn't that just be:
dProfits/dprice = (# sold)
My calculus is a little rusty, so any tips are very much appreciated. Or if there's something I'm missing about the profit equation, or if there's some algorithm I could use in this situation.