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A model in the LINGO optimization modeling language
of the multi-dimensional knapsack problem;
The one dimension knapsack problem is:
Given
a container (the knapsack) of given size or capacity, and
a set of candidate items, each with a given value and size,
Choose which items to place in the knapsack so as to:
Maximize the sum of the values of the items placed in the knapsack,
subject to
the sum of the sizes of the placed items does not exceed knapsack size.
Variations of the knapsack items appear in many applications.
The loading or packing of a truck, cutting required smaller lengths of steel rods
or cables from a longer stock length,
cutting wide stock rolls of paper into smaller customer requested sizes,
which songs to place on the side of a musical record of limited size, etc.;