Job scheduling Consider the problem of scheduling $n$ jobs of known durations $t_1,$dots,$t_n$ for execution by a single processor. The jobs can be executed in any order, one job at a time. You want to find a schedule that minimizes the total time spent by all the jobs in the system. $($The time spent by one job in the system is the sum of the time spent by this job in waiting plus the time spent on its execution.$)$

Design a greedy algorithm for this problem. Does the greedy algorithm always yield an optimal solution?