Understanding the unbounded knapsack problem

Unlike the 0/1 Knapsack Problem, many real-world optimization problems allow the same option to be used an unlimited number of times rather than restricting each choice to a single use. In these situations, the decision is not simply whether to include an option or not, but how many times it should be chosen while still respecting the overall capacity constraints. Each option has an associated cost and value, and the objective is to determine the combination that maximizes total value without exceeding the available capacity.

A fundamental problem in this space is the unbounded knapsack problem, where "unbounded" means that each choice can be included an unlimited number of times.