The knapsack problem is a problem in combinatorial optimization: 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. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision-makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897.[1] The name "knapsack problem" dates back to the early works of the mathematician Tobias Dantzig (1884-1956),[2] and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage.
If you are nomad and live out of one carry-on bag. This means that the total weight of all your worldly possessions must fall under airline cabin baggage weight limits - usually 10kg. On some smaller airlines, however, this weight limit drops to 7kg. Occasionally, This raises the difficulty to decide not to bring something with you, to adjust the smaller weight limit. As a practical exercise, deciding what to leave behind (or get rid of altogether) entails laying out all our things and choosing which ones to keep. That decision is based on the item's usefulness to us (its worth) and its weight.