Show how you will model the above problem using the problem of Bipartite Matching. Also, what property of the Bipartite Matching problem captures the fact that all tasks have been assigned time slots?
I've said that it could be modeled by putting tasks on one side and intervals on the other, where each time slot can have only one task but the tasks themselves could have more than one time slot. So we would get a graph like this:
Assign a node to each task and a node to each time $1...,n$ and connect each task node $i$ with the time node in each interval from $s_i$ to $t_i$. Now you need a maximal matching. So what you did is correct except that a time can have many task nodes pointing to it. The matching is needed when you have to make a decision between overlapping things ands that’s the essence of the problem. You can think of the problem like an analogy between this and a dating site: every task favors a time interval // a girl likes many guys(equally), every task can only occupy one time slot // every girl has to choose one guy, time nodes have multiple tasks pointing at them // a guy is liked by multiple girls, find the maximum number of tasks that can be scheduled // pair up as many girls(&guys) as possible.