1. Determine whether you can feasibly schedule the following task se ts using the RM (rate-monotonic) algorithm. If yes, provide a schedule. If no, justify your answer and provide an EDF schedule if possible. Task 1: c = 3, p = 8; Task 2: c = 3, p = 9; Task 3: c = 3, p = 15 2. Determine whether there is a feasible schedule for the following set of periodic processes. If yes, show the schedule and the steps used to derive it. $T_1$: $c_1~=~1,~d_1~=~p_1~=~14$. $T_2$: $c_{21}~=~1,~c_{22}~=~3,~d_2~=~6,~p_2~=~7$. $T_3$: $c_{31}~=~2,~c_{32}~=~3,~d_3~=~14,~p_3~=~14$. $T_2$ must rendezvous with $T_3$ after the first scheduling block of $T_2$. $T_3$ must rendezvous with $T_2$ after the first and second scheduling block of $T_3$. 3. Plot the following single-instance tasks on the scheduling game board. task 1: $c_1~=~4,~d_1~=~5$ task 2: $c_2~=~5,~d_2~=~5$ task 3: $c_3~=~1,~d_3~=~3$ task 4: $c_4~=~3,~d_4~=~8$ Suppose two processors are available for executing these tasks. If schedulable, show a feasible schedule, either a sequence of game boards or a timing diagram/Gantt chart. If not, explain. 4. We have assumed in lectures that context-switching due to preemption incurs no overhead. Now suppose context-switching (from one task to another) requires $x$ time units. Consider a system with 2 tasks with computation times $c_1$, $c_2$, and periods $p_1$, $p_2$ (which are equal to their deadlines and $p_1$ is less than $p_2$). Derive the maximum value of $x$ for which this task set is scheduable by the RM algorithm. Show calculations.