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The knapsack problem is a classic combinatorial optimization problem that models decision-making processes aimed at maximizing benefit under limited resources. It derives its name from the metaphor of packing the most valuable items into a bag with a fixed carrying capacity. The problem first gained attention in 1957 through the work of M. D. Weingartner and was later formalized mathematically in the 1960s through research by George Dantzig on linear programming. Problem Definition The knapsack