0/1 Knapsack - Why Greedy Fails

In $0$/$1$ knapsack, items are indivisible. Greedy by ratio fails.

Example: items = [(60,10), (100,20), (120,30)], W = $50$. Greedy: take item $1$ (ratio P2), item $2$ (ratio P4). Total weight: $30$, value: $160$. Item $3$ does not fit.

But items $2$ + $3$: weight = $50$, value = $220$. Better! The discrete constraint causes blocking. Use DP for $0$/$1$ knapsack.