I'm an accountant for two companies. One pays the other a commission that is intended to equalize their operating income ratios.
Operating Ratio = Operating Income/Revenue
CompanyA pays the commission to CompanyB. CompanyA is also much larger. When CompanyA pays commission, the commission becomes an expense to CompanyA and revenue to CompanyB.
The sticky part I need calculus help for is determining what that percentage is. Say for example:
Revenue - 1,000,000
Expense - 600,000
Operating Income - 400,000
Operating Ratio = 400,000/1,000,000 = 40%
Revenue - 150,000
Expense - 120,000
Operating Income - 30,000
Operating Ratio = 30,000/150,000 = 20%
I want CompanyB to match the operating ratio of company CompanyA, so I pay CompanyB another 30,000 in commission which brings CompanyB to 40% operating ratio. The problem is, that 30,000 becomes an expense for CompanyA, which brings its operating ratio down to 37%.
I would need to do this readjustment multiple times for each to find a matching operating ratio.
I figure there's an easy answer using calculus but I can't remember how to go about it (it's been over a decade).