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(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all but the green box.
) The knapsack problem or rucksack problem is a problem in: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.. The name 'knapsack problem' dates back to the early works of mathematician (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage.. It derives its name from the problem faced by someone who is constrained by a fixed-size and must fill it with the most valuable items.. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.
The problem often arises in where there are financial constraints and is studied in fields such as,,,,, and.. Example of a one-dimensional (constraint) knapsack problem: which boxes should be chosen to maximize the amount of money while still keeping the overall weight under or equal to 15 kg? A could consider both the weight and volume of the boxes.
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