Q$4$d$\_($i$)$ and a duration I$\_($i$)$ which is the time it takes

to complete the job. You can't do two jobs at the same time. The lateness is given by t$\_($i$)-$l$\_($i$)$

where t$\_($i$)$ is the completion time of job i$.$ The objective is to minimize the maximum lateness

across all the jobs.

Example: d$\_(1)=50$I$\_(1)=20,$d$\_(2)=20$I$\_(2)=5,$d$\_(3)=40$I$\_(3)=30,$ If the jobs are scheduled in order $(1,3,2)$

maximum lateness is $35.$

Greedy algorithm $1$: Schedule the jobs in increasing order of their duration $($l$\_($i$)).$

Greedy algorithm $2$: Schedule that job first whose deadline is the closest.

Greedy algorithm $3$: Schedule that job first for which d$\_($i$)-$ I$\_($i$)$ is the smallest.

Which of these algorithms work? Give at least one example to show that an algorithm doesn't

work.