Creating an Equation for my Online Store

Question

I have a site that I am building and I am trying to figure out how much to charge customers. I want to go as low as possible while maintaining a certain profit margin.

Here are the perimeters: I want 10% of every sale to go the company for profit/operating costs. The credit card processor takes 3% + 0.33 (cents) on every transaction.

How do I find how much to increase the products cost and keeping everything balanced?

Example:

(150 * 1.13) + 0.33 = 169.83 --Retail Price

(169.83 * 0.03) + 0.33 = 5.4249 --Credit Card Process Fee

(168.83 * 0.1) = 16.983 --10% Profit

169.83 - (5.4249 + 16.983) = 147.4221 --Ammount Left After Costs

147.4221 < 150

13% increase is not enough to meet profit margin.

I was able to find an exact percentage to increase the original cost when x = 150, which is 15.1954023%, but I can't manually do this for every product as I could have hundreds/thousands with many different pricing options.

Thanks in advance. Any help is useful, even if you tell me it's not possible at all (at least then I will know).

Answer 1

Let's try reasoning backwards. Let $P$ be the original product price and $S$ the desired sale price. Then:

• We start with the price of $S$ that you charge your customers;
• $10\%$ of $S$, i.e. $0.1S$, goes to your profits and operational costs;
• $3\%$ of $S$ plus another $0.33$ (cents), i.e. $0.03S+0.33$, goes to the credit card company.

Since you want to keep your price as low as possible, after taking away these expenses you should end up with original product price: $$S-0.1S-(0.03S+0.33)=P.$$

Solving this equation for $S$ we find that $$0.87S-0.33=P \implies S=\frac{P+0.33}{0.87}.$$