As I see it you basically have 13 equations plus six constraints (all coefficients >0) but just six variables to play with.
Yes, I guess it is 13 equations, not 2. Don't know what I was thinking when I said 2 
Its not clear to me why you think that there exists a satisfactory solution to your problem, that is, why you think you can get fideal using a linear combination of the other six f's with coefficients summing up to 1.
There is a best fit (least squares) solution. I can see why Gary wants to do this, but what I don't see is how fideal could be defined in the first place. What is the optimum balance of funds with different size and value/growth ratings?
Yes, I guess it is 13 equations, not 2. Don't know what I was thinking when I said 2
And I had already typed (and sent) in my answer something about that "the problem still remains that there are only 2 equations and ..". Somehow it dawned on me then that this may not be true 🙂
There is a best fit (least squares) solution. I can see why Gary wants to do this, but what I don't see is how fideal could be defined in the first place. What is the optimum balance of funds with different size and value/growth ratings?
Maybe I should have read Gary's first post more thoroughly. As I understand it now it is mandatory that the coefficients (being percentages) add up to 1 and I guess the in every matrix f the left 3x3 should add to 100 as should the last column. Thats true for fideal but not not for the others. I changed the values slightly to ensure that and solved for just the first 5 coefficients, the last being the complement to one.
I encounter some strange effects: If the "weight" of the last two constraints are not the same or if I change the order by moving the first one a bit downwards, the solution changes significantly and the left 3x3 values don't add up to a perfect 100 anymore. Especially the last effect is inexplicably to me, as the 6 coefficients still would add up to a perfect 1.
