I've got a problem with getting optimized solution from this task:
We have n customers, which buy articles from m suppliers. There are much more customers and suppliers on the market. We've got sales data from the m suppliers concernig total market. We want to find a mix from our customers which best represents the market.
Example:
Customer Supplier A Supplier B Supplier C Total
4711 10 30 10 50
4712 20 40 40 100
4713 5 11 9 25
Total 35 81 59 175
% 20% 46% 34% 100%
From our supplies we know:
Supplier A Supplier B Supplier C Total
5000 1500 7000 13500
37% 11% 52% 100%
My idea was to find $$ f = \min( \sum_{k=0}^m(T_k - S_k)^2) $$ where $$ T_k = \sum_{j=0}^n{x_j} * \frac{Customer_{j,k}}{\sum_{i=0}^mCustomer_{i,j}} \hspace{20mm} x_j = {<0,1>} $$ and $$ S_k = \frac{Supplier_k} {\sum_jSupplier_j} $$
I have lpsolve55.dll, but how can I construct input data for it?
Regards, Gabriel