Exercise $15\mathrm{.}1-3$:

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

mutually compatible activities. 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. Do the same for the approaches of always selecting the compatible activity that overlaps the

fewest other remaining activities and always selecting the compatible remaining activity with the

earliest start time