Given $n$ objects $o_i$ with weight $w_i$ and value $v_i$ how do we maximise the value of a bag that can carry weight $B$. The solution to this is a subset of objects $S \subset \{1, 2, \ldots, n\}$ such that:

• $\sum_{i \in S} w_i \leq B$, and
• it maximises its value $\sum_{i \in S} v_i$.