If a number can play the same as a vector in LP

I have a simple linear program as below:

$min L(x)=\sum_i w_i x_i$

subject to

EDIT:

$a\leq f(x_i) \leq b$

where $w_i$ are constants and known calculated by $w_i=(v1_i).*(v2_i)\ \forall i$, where $v1$ and $v2$ are two simple vectors and $.*$ denotes element-wise multiplication (the same meaning of $.*$ in MATLAB). I want to use a simple number like $V\in R$ instead of $v1$, such that the result of original LP does not change (or the objective function L(x) changes very low). In other words I want a real number $A$ can do the same job of the vector $v1$ in terms of LP solution.

Thanks

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I don't quite understand what you are asking. Cn you please clarify your question. However, the solution will always be $x_i=a_i$ if $w_i> 0$ or $x_i=b_i$ if $w_i< 0$. If $w_i=0$, then $x_i$ can be any number in the given range. –  Daryl Nov 30 '12 at 20:01
Thank you for your reply. I edited the constraint, I don't want the solution of the LP, but I want to change $v1_i$ to a real number A, to do the same job of $v1_i$, i.e the solution does not change very much. I think there must be a number A such that the correlation of $A.*v2_i$ and $v1_i.*v2_i$ be as high as possible to change the coefficients (and the relation between them) as low as possible. –  remo Dec 1 '12 at 4:41