Knapsack Problem

Problem Definition

Given a set of $n$ items $X$, size $s_i\ge 0$, values $v_i\ge 0$, a weight limit $B$, and a target value $V$, is there a subset $S\subseteq X$ such that: ${\sum }_{i\in S}{s}_i\le B$ and ${\sum }_{i\in S}{v}_i\ge V$

Prove Knapsack problem is NP-complete

1. Prove Knapsack problem is NP.
2. Choose Subset Sum Problem
3. Prove that Subset Sum Problem ${\le }_P$ Knapsack Problem. Given Subset Sum instance $w_1,\cdots ,w_n$ and an integer $W$, set $s_i=v_i=w_i$ and $B=V=W$.