$1)$ Consider eight jobs and three identical machine problem. Generate randomly different processing times for each job. The process times must be integer number between $5$ and $25($at least two of them must be less than $10$ and two of them must be greater than $20).$ Answer the following questions and draw Gantt chart for each solution. $($a$)$ Apply the LPT$-$List Heuristic Algorithm to minimize the makespan, and check its optimality. $($b$)$ Determine the optimal schedule that minimize the total completion time. Suppose we now have three parallel machines with different speeds. Generate randomly different speed for each machine in the same problem. The speeds must be integer number between $1$ and $5.($C$)$ Apply the algorithm given in lecture to minimize the total completion time problem. $($d$)$ Suppose preemptions of jobs have been allowed. Apply the SRPT$-$FM rule to minimize the total completion time.