No it's not calculus, just put letters for the variables, and equate the two ratios, maybe like so...
Now plug in the given numbers, but including the commision, x...
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).