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For questions related to the knapsack problem that seeks to find the number of each item to include in a limited container (in an integer knapsack or whether to include an item in a binary knapsack), given each item's weight and value, with the goal of maximizing the total value.

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integer programming relaxation problem

How can the formulation of $P2$ guarantee that it is a relaxation of $P1$? (if $w=0$, $1$ is much bigger than $2$).
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