Activities: [(, , ), (, , ), (, , )]. Greedy by end time: (1,3) then (4,6). Total: + = . Alternative: just (2,5). Total: . Worse. Greedy wins again. Let me find a real counterexample..
Activities: [(, , ), (, , ), (, , )]. Greedy: (0,4) then (4,7). Total: . Alternative: (3,5) alone. Total: . Tie. The point: with weights, the greedy choice property can fail. Use DP for weighted cases.