Consider the problem of scheduling $n$ jobs of known durationst $1,t2,$dots,$tn$ for execution by a single processor. The jobs can be executed in any order, one job at a time.

a$)$ Design an algorithm 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.$)$

b$)$ Design a greedy algorithm for this problem.

c$)$ Does the greedy algorithm always yield an optimal solution?

d$)$ Analyze your algorithm and give the results using order notation.

give pseudo code for a$)$