Maybe the title is not clear, so let me explain:
I have a product with several options, each option changing the price (increasing or decreasing it):
- Winter Boots + Red + Small + Leather = 105$
- Winter Boots + Red + Small + Down = 125$
- Winter Boots + Green + Small + Leather = 85$
- Winter Boots + Green + Small + Down = 105$
- Winter Boots + Red + Big + Leather = 110$
- Winter Boots + Red + Big + Down = 130$
- Winter Boots + Green + Big + Leather = 90$
- Winter Boots + Green + Big + Down = 110$
Given all this data, I want to find the base price and how much each option adds or subtracts from it
For example, the result should find base price being $100
The Red option adds $10
The Small option takes away $10
The Leather option adds $5
And so on for every option (Red, Big, Down)
These equations are very redundant, which means there are lots of solutions.
To see this, note, happily, that each variable begins with a different letter. We note from the first pair that $$D-L=20\;\;\Rightarrow D=L+20$$. Similarly, the first and third equations tell us that $$R-G=20\;\;\Rightarrow R=G+20$$
Similarly, the first and fifth equations tell us that $$B-S=5\;\;\Rightarrow B=S+5$$
If we now specify $L,G,S$ at random then $D,R,B$ are determined and we can solve for $$W=85-(L+G+S)$$
Nor does it help much to specify $W$ externally. As you can see from the above, that just amounts to knowing $L+G+S$ so you'll still have two degrees of freedom.