I have some knowns and unknowns and can't seem to do the calculus. So, I'm going to take a break and in the meantime see if I can't get some help.

I have the following data: Volume, Total Margin, % Sold thru Channel A, and % Sold thru Channel B. I need to determine unit and total margin for both Channels. I also know that my $/unit margin for Channel A is twice what it is for Channel B.

E.g., Volume = 100 units, %A = 50% @ $.50/unit, %B = 50% @ $.25/unit. So 50 units sold Channel A @ $25 and 50 units sold Channel B @ 12.5, for a total Margin of $37.5

Now, if I have Volume = 100 units and %A = 75%, %B = 25% and I know my total margin is $100, what is my margin for Channel A and Channel B on a per unit and total basis?

Can someone create a formula based on %A and %B sold for X Total Volume and Y Total Margin, what would be the unit and total margin for Channel A and for Channel B? What if the margin relationship changes and that relationship is Z? E.,g., now unit margin A = 2 * unit Margin B

> Now, if I have Volume = 100 units and %A = 75%, %B = 25% and I know my total margin is $100, what is my margin for Channel A and Channel B on a per unit and total basis?

It's not solvable for two unknowns. There are an infinite amount fo solutions

Until you fix say A or B margin, then you can't calculate the other

Volume = 100 units -> n
%A = 75% @ x $/unit
%B = 25% @ y $/unit
Total Margin = $100
(x * (n * 75%) + (y * (n * 25%)) = 100
The relationship between x and y is: x = y + y
((y+y) * (n * 75%)) + (y * (n * 25%)) = 100
((y+y) * (100 * 75%)) + (y * (n * 25%)) = 100
((y+y) * 75) + (y * 25) = 100
75y + 75y + 25y = 100
y(75+75+25) = 100
y = 100 / 175
y = 0.57142857142857142857142857142857
Then y + y = x = 1.1428571428571428571428571428571

Now let's apply this on the first example:
Volume = 100 units -> let's assume it's n
%A = 50% @ $.50/unit -> let's assume x = $/unit A
%B = 50% @ $.25/unit -> let's assume y = $/unit B

(x * (n * 50%) + (y * (n * 50%)) = 37.5
x = y + y
((y+y) * (100 * 50%) + (y * (100 * 50%)) = 37.5
((y+y) * 50) + (y * 50) = 37.5
50y + 50y + 50y = 37.5
y(150) = 37.5
y = 0.25
x = 0.25+0.25
Then (x=0.5) (y=0.25)

JimyX was first and complete with spreadsheet. brettdj helped see the same approach in a different light. Excellent collaboration and thanks!

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It's not solvable for two unknowns. There are an infinite amount fo solutions

Until you fix say A or B margin, then you can't calculate the other

Cheers

Dave