# Need help to find a formula for math problem for anticipation of event according to several variables

To make it simple, I am looking for a formula to get as much control as possible over a business:

I am using online advertisement (I have to pay for it) to advertise and generate sells of a product, and I am trying to find out a formula that would help me to predict what prices I should spend on ads to get the maximum profit possible considering all the variables in this business.

These variables are:

• Budget (the amount of money I will spend daily on ads)
• Cost per acquisition (the average money you have to spend to get 1 sell)

• Product price (the price at which the product is bought)

• Product resell price (the price at which the product is sold to my customers)
• Margin (product resell price - product price)
• Sales revenue (product price * number of items sold)
• Net profit ((margin * number of items sold) - taxes)
• Taxes (20% of sales revenue)
• Return over investment (also named ROI. = (Net profit / ad spent) * 100). For example (3000 / 500) * 100 = 600% ROI.

If I increase the budget, the cost per purchase will increase proportionally as the audience the ads are made on becomes broader and less targeted, so ROI will go down, but it is the only way to earn as much money as I could from these ads.

I have to find a formula that could help me to determine: What maximum budget should I spend to get the best net profit in relation to the cost per acquisition and the proportional (or not) increase of cost per acquisition in relation to budget increase?

Do some of you have an idea of how I could do this please?

Thanks!

• If resell price $<$ 1.2 times product price, the optimal budget is zero. – Hagen von Eitzen Jun 19 '17 at 5:46