than or equal to the knapsack's capacity.

The bounded knapsack problem (BKP) removes the restriction that there is only one of each item, but restricts the number of copies of each kind of item to a maximum non-negative integer value :
: maximize
: subject to and

The unbounded knapsack problem (UKP) places no upper bound on the number of copies of each kind of item and can be formulated as above except that the only restriction on is that it is a non-negative integer.
: maximize

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