Is my Math Equasion Solvable?

Question

Hi

I am trying to figure out what my m minimum selling price should be for me to make a 20% margin

Here's what goes into the calculation:

Purchase Price (P) - fixed $
Sales Tax (T) - Fixed % - 17% of selling Price
Commission (C) - Fixed % - 12% of selling Price
Shipping - Fixed $
Margin - Fixed % - 20% of selling Price

So let's say the Purchase price is $10 and the shipping $2 what is the absolute minimum I can sell this for and still make 20% on my selling price? A slight complication is the commission can't go below $0.4

 

I'm normally fairly good wioth math but on this I'm struggling - is it solvable?

 

Thanks in Advance

 

Dean

 

 

 

Answer 1

Yes it is solvable. You have

 

Price - Cost - shipping - tax - commission = .20*price

P -10 - 2 - .17P - .12P = .2P

 

P - .29P = .2P + 12

.71P - .2P = 12

.51P = 12

P = 12/.51 = 23.53

 

23.53 - 12 - 4 - 2.82 = 4.71

 

23.53 * .2 = 4.71