Okay guys. It looks like my initial problem and later explanation were quite misleading. Let me try again.
First, This is NOT a homework problem. I am a graduate and don't really wish to go back to school so soon again.
Here is the complete problem. I need to prioritize from set of objects based on the following equation.
R(Object) = (Ax + By + Cz) / (A + B + C)
where x, y, and z are properties of this object and A, B and C are their corresponding weights (how important is this particular property ?)
My approach to the problem was to prepare a finite data set for different values of x, y, and z and then fill this data-set with approximately close values for R(Object) (or better of a range in which the R(Object) should fall [kmin, kmax]).
As an exmaple consider this. I am a seller and I have 4 apples. Apples have 3 properties namely ripeness, redness and size. Every buyer will have different criteria for selecting one from the 4 possible apples. Some might prioritize the size of the apple above its redness and other might consider the ripeness over everything else. These "selection criteria" will act as weights (namely, the A, B and C) for the individual property of the apple. Depending on these weights, the R(apple) will be different for all 4 apples for any given customer (A, B and C are the same for any particular customer) and will result in a different apple chosen by different buyer. Also, as time passes, the values of these properties might change. NOTE: The weights chosen for individual property by any customer always remain the same (even over time).
So, Yes ReedBeta is right. I have a whole set of x, y, z data set. I fill in a R(Object) value for a given set of x, y, and z. I need to find A, B, and C so that they satisfy the complete data set.
Until yesterday, I used to tweak these weights myself to get a descent selection behavior but as the number of properties per object and customers increase this is becoming too time-consuming process.
Hope the example should help explain the problem.