Problem $16\mathrm{.}1-3$ on p$422.$

Not just any greedy approach to the activity$-$selection problem produces a maximum$-$size set of

mutually compatible activities.

$($a$)$ Give an example to show that the approach of selecting the activity of least duration from

among those that are compatible with previously selected activities does not work.

$($b$)$ Do the same for the approach of always selecting the compatible activity that overlaps the

fewest other remaining activities.

$($c$)$ Do the same for the approach of always selecting the compatible remaining activity with the

earliest start time.