Relationship between cost margin and sales volume

I was speaking to a wine director about the value of running a lower wine markup for the sake of achieving higher sales volume. Very few restaurant operators think about this relationship in a sophisticated way. They usually just pick a number and say please give us a cost of goods sold of 30%...

The fundamental question is for every X points you increase your cost of goods sold, how much can you increase sales volume?

As an example if you sell $100,000 of wine a month at a 30% COGS, that will give you a net profit of $840,000 per year from wine. If you think by running a 33% COGS you can increase sales by 15%—just to toss out an idea—you have a net profit of $964,800 dollars per year. That's $124,800 a year more in the owner's pocket.

If I did my math right, you would only need to increase wine sales by more than 4.4% to see an increased profit if you change your COGS from 30% to 33%. This does not even take into account the potential for increased food sales from a higher guest return rate if they perceive more value.

My first point in creating this post is that everyone should be aware of this.

My second point in this post is whether any math geniuses out there want to create some simple equations for analyzing the relationship between COGS, Volume and Net Profit.