Its decision version was proved to be NP-complete by reducing the exact cover problem to it.  
The iterated version of it was solved by Ernie Brickell in 1984 using a Cray-1, and a special case of it is used in the currently unbroken Chor-Rivest public key system. Its decision version was proved to be NP-complete by reducing the exact cover problem to it.  One special case of it is the decision version with the constraint that the cost equals the value, and is equivalent to asking whether there exists a subset of a set of integers which has a given sum. For 10 points, name this combinatorial optimization problem, whose simplest formulation gives a set of items, each with a different weight and value, and asks you to maximize the value while being able to fit them in a certain bag.
The iterated version of it was solved by Ernie Brickell in 1984 using a Cray-1, and a special case of it is used in the currently unbroken Chor-Rivest public key system.
Knapsack problem