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

Thanks -

Dave

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 * %A) + y * (n * %B)

0.5 * (100 * 50%) + 0.25 (100 * 50%)

25 + 12.5

= 37.5

Total Margin is $37.5

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 = 0.571428571428571428571428

Then y + y = x = 1.142857142857142857142857

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)