The applied mathematics of optimizing market baskets using information in efficient shopping list's involves what have come to be known as packing problems. Here we will attempt to formalize one type of packing problem of interest to the pub wan movement, that of optimizing a market basket of packaged edible goods according to a norm spec à la sample grocery normspec. Let's assume we have m product packages to choose from, and n nutrients (or chemical constituents) that have been tabulated for the m products in question. Then for each 1≤i≤m and 1≤j≤n we have the following vectors and matrix:
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