Credit card processor charges, for each transaction, $2.9\% + \$0.30$.
I need to find an amount that covers that cost, from $\$5$ to $\$5,000$, on a per item basis, all while maintaining a small profit.
For example, a customer may want to purchase 3 items. Each item has a different price and possibly a different fee structure based on whether or not it's a for-profit purchase or non-profit purchase.
Item 1 is $\$10$ and for-profit so we need to account for the processing fee plus a $5\%$ profit.
Item 2 is $\$80$ and for-profit so we need to account for the processing fee plus a $5\%$ profit.
Item 3 is $\$25$ and non-profit so we need to account for the processing fee only- no profit.
What I cannot determine is a full-proof way to account for the fees all the way up to $5,000 without losing money on the processing fees.
I will ignore dollar signs. Suppose that $C$ is the cost of the product and we wish to charge $C + X$ for the product. The processing fee is $.029(C + X) + .3$. We need to solve $$(C + X) - (.029(C + X) + .3) \geq C$$ for $X$. In this equation $C + X$ is what we charge and $.029(C + X) + .3$ is the processing fee. If the difference is greater than $C$ we make a profit. There are probably other costs that are not mentioned in this problem. Presumably they are included in the value of $C$. In any event we need $$.971 X \geq .029 C + .3.$$ We can solve for $X$ as follows: $$X \geq \frac{.029 C + .3}{.971}.$$ There is no upper bound for the value of $X$.