Problem $1.$

Below are some alternative ways to approach the activity$-$selection problem using a greedy strategy.

For each one, state whether it yields an optimal solution and give a counterexample if it doesn't.

$($a$)$ Select the activity of least duration $($from those that are compatible with already$-$selected

activities$).$

Solution:

$($b$)$ Select the activity with the latest start time that is compatible with all previously selected

activities.

Solution:

$($c$)$ Select the compatible remaining activity with the earliest start time.

Solution: