/ knapsack: items have weight and value, capacity is limited, items are indivisible. Maximize value. Greedy by value/weight ratio seems natural. But it fails.
Items: (weight= P0, value= P1), (weight= P2, value= P3), (weight= P4, value= P5). Capacity = . Ratios: , , . Greedy takes item (ratio P11), weight used. Remaining capacity . Item does not fit. Item fits. Total value: + = . But taking just item gives value with weight . Wait, that is less. Let me try again..