Question: Consider a system that has two CPUs $($hard cores$)$ and each CPU can appear to the operating system as $2$ execution engines $($hyper$-$threading allows the operating system to assign $2$ concurrent executions to a single physical core, so in this case, up to $4$ execution engines could be run in parallel$).$ Suppose three programs, P$0,$ P$1,$ and P$2$ are started with run times of $5,10$ and $20$ msec, respectively. Assume that all three programs are $100\%$ CPU bound, do not block during execution, and do not change an execution engine once assigned by the operating system. If all $3$ executions are queued for execution by the operating system at the same time $($each execution engine has its own dispatch queue of processes ready to run$)$:

A$.$ What is the shortest elapsed time required for the completion of all three executions $?($explain the scheduling that could be used to get this result$).$B$.$ What is the longest elapsed time required for the completion of all three executions $?($explain the scheduling that could be used to get this result$).$