Items: (weight= , value= ), (weight= , value= ), (weight= , value= ). Capacity = . Ratios: , , . Greedy takes item or first (ratio ), say item . Weight used: . Item also fits. Total: + = .
But taking item alone uses weight and gets value . Then item or ? Item has weight , but + = > . Does not fit. Hmm, greedy got , item alone gets . Greedy wins here. Let me find a real counterexample. Testing examples helps you understand when greedy breaks.