Attached is a spreadsheet with two accounts. Each account has the same retail and invoice. One school has a small enrollment and the other has a larger enrollments. There is a handling fee of $2 per enrollment. There are only two variables that can be changed: brochure cost & incentives. Also, the larger the enrollment, the larger the brochure cost. Brochure Cost can be reduced only a certain amount. The cheapest it can be reduced is 110% of # of students. So for John Spicer, the Brochure Cost could be reduced to 683.10 (621 students x 1.10 = $683.10)
The goal is to reach a 36% gross profit margin...which is (profit / invoice). Profit is Invoice - Total Expenses
There should be a way to figure a lump sum of the amount you have to spend on brochures and incentives. For example of Spicer, you can spend $843.10 on brochures and incentives....which is $683.10 on brochures and $160.00 on incentives.
I can figure adjust brochure cost & incentive cost to reach the 36% but I know there is a formula to make it easier.
In order to solve this problem, let's first write the definitions of Total Expenses, Profit and Gross Profit %.
Total Expenses = Brochure Cost + Product Cost + Freight Cost + Prizes + Incentives +
+ Techer Gifts + Samples + PackOut + Delivery + Handling
Profit = Invoice - Total Expenses
Gross Profit % = Profit/Invoice
You are interested in finding the sum of Brochure Cost + Incentives such that the gross profit percentage is 36%. Since you mentioned that costs that are not brochures or incentives are "fixed" ...
This solution is comprised of a detailed explanation to determine variable of gross profit %.