# Creating a model of two factors with synergy

Hi dear mathematicians,

I'm currently trying to create a simple generic model in Excel where I use synergy effects between two factors. For example, the price of a product is determined by two factors - uniqueness and importance. If the product have high uniqueness it will be more expensive and if the product is of high importance for the buyer it will be more expensive. The effect of importance is quite small if the uniqueness is low since you can just buy the product from another supplier. However, if the product is both unique and of high importance this will create a synergy effect which will increase the price since the seller has great power. Below is a quick example where importance is on the vertical axis and uniqueness is on the horizontal axis (just made up some numbers to illustrate the effect):

1    2    3
1.1  4   10
1.2  8   50


Earlier when I didn't had the trouble of synergy I used the formula p=I*U to calculate he price p with importance I and uniqueness U. Now the formula would be p=I*U*s(I,U) where s is the synergy effect coefficient as a function of s(I,U). What I need help with is how to calculate s(I,U).

This is not an Excel question, it's more how I solve this mathematically.

Any ideas on how to solve this problem? Any help would be appreciated. And sorry if I tagged it wrong, I'm new here.

Thanks!

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I've changed algebra tag to algebra-precalculus, since we don't use algebra tag anymore, see meta for details. (Of course, feel free to retag the question again if you find a more appropriate tag.) – Martin Sleziak Aug 24 '12 at 6:12

You might try $s(I,U) = a + b I^p U^q$ for some positive constants $a,b,p,q$. Perhaps $p=q=1$ if you want to keep it simple.