Revenue goal seeking with multiple goals but only 1 variable

Nycgirl96

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WWYD - goal seeking for multiple knowns that have with multiple goals, but can only be manipulated using 1 variable

WWYD - goal seeking for 2 known numbers with 1 variable.

So there's a dilemma I'm trying to figure out different approaches to. It looks like this. You have A and B and the goal for A is 2A and the goal for B is .75B, but only one number can be applied to both A and B, when both are considered together. This should also be applicable to 5 know variables (Ie A B C D E, and their respective goals). The goal is to Maximize revenue, without charging obscenely.

Ex.) A and B are fees associated with every $10 person A, B makes. A=.14 with a goal of .28 and B=.32 with a goal of .55 - you can't apply 100% increase because that would give you the .28, but that would be too high for B at .64. 80% on the other hand would give you .26 and .58 - much more reasonable in regards to the goals. If you add C into the equation where C = 2.00 and it's goal is 2.35, where do we go from here? We don't want to raise C at the same rate as A and B, because C gives us more revenue than A+B.

I've luckily been able to find a set of ratios to multiple by, but these numbers stemmed from wonky math (average difference between the variables, taking that as the min., "creating" a normalized chart of the variables using statistics etc.) but I want to explore something that actually has foundation in theorem and reality. Now doing averages of goals, and multiplying the std dev of the base variables by some ratio.

right now I'm doing weighted average of the goals % with respect to the sum of the variables (I.e., what weight is 2.15 with respect to 2.15+.14+.32?) then multiplying the goals times that weight and taking the average of that.

Open to any type of math not passed Linear Algebra.
 
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