$10\mathrm{.}7.$ This problem demonstrates that although Equation $(10\mathrm{.}2)$ for rate monotonic scheduling is a sufficient condition for successful scheduling, it is not a necessary condition $($i$.$e$.,$ sometimes successful scheduling is possible even if Equation $(10\mathrm{.}2)$ is not satisfied$).$

a$.$ Consider a task set with the following independent periodic tasks:

Task $P_1$:$C_1=20$;$T_1=100$

Task $P_2$:$C_2=30$;$T_2=145$

Can these tasks be successfully scheduled using rate monotonic scheduling?

b$.$ Now add the following task to the set:

Task $P_3$:$C_3=68$;$T_3=150$

Is Equation $(10\mathrm{.}2)$ satisfied?

c$.$ Suppose the first instance of the preceding three tasks arrives at time. Assume the first deadline for each task is the following:

$D_1=100$;$D_2=145$;$D_3=150$

Using rate monotonic scheduling, will all three deadlines be met? What about deadlines for future repetitions of each task?