Consider a system that has fi ve periodic tasks, A , B , C , D ,and E , and three processors P 1 , P 2 , P 3 . The periods of A , B ,and C are 2 and their execution times are equal to 1. The periods of D and E are 8 and their execution times are 6. The phase of every task is 0, that is, the fi rst job of the task is released at time 0. The relative deadline of every task is equal to its period. (a) Show that if the tasks are scheduled dynamically on three processors according to the LST algorithm, some jobs in the system cannot meet their deadlines. (b) Find a feasible schedule of the fi ve tasks on three processors. (c) Parts (a) and (b) allow us to conclude that the LST algorithm is not optimal for scheduling on more than one processor. However, when all the jobs have the same release time or when they have the same deadline, the LST algorithm is optimal. Prove this statement.