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$).$

Consider a task set with the following independent periodic tasks:

Can these tasks be successfully scheduled using rate monotonic scheduling?

Now add the following task to the set:

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

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

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