On a serial computer, portion A of program Q takes $12$ s$,$ while portion B takes

$98$ s$.$ On a parallel computer, portion A speeds up by a factor of $2\mathrm{.}135,$ while

portion B speeds up by the number of processors. If a fractional number P$*$ of

processors exactly achieves a speedup that is a fraction f $<1$ of the

theoretical maximum speedup, then P$*$ processors also exactly achieve a run

time that is a fraction $1/$f $>1$ of the theoretical minimum run time, and

conversely.

a$)$ How many fractional processors P$*$ are required to achieve $45\%$ of the

theoretical maximum speedup? Answer to five decimal places. How many actual

processors P are required to achieve at least $45\%$ of the theoretical maximum

speedup?