Variant - Weighted Activity Selection

What if activities have weights (profits)? Maximize total weight of selected activities.

Example: activities = [($1$, $4$, $3$), ($3$, $5$, $2$), ($5$, $7$, $4$)]. Weights: $3$, $2$, $4$. Greedy by end time: (1,4) then (5,7). Total weight: $3$ + $4$ = $7$. Alternative: (3,5) then (5,7). Total weight: $2$ + $4$ = $6$. Greedy wins here.

But with different weights, greedy can fail. Weighted activity selection needs DP. The weight breaks the greedy property. A low-weight activity ending early might block high-weight activities.