$(1)$ Assume a sequential program takes $1,000$ seconds, what is the maximum speedup possible according to Amdahl's Law for a program that is $10\%$ inherently serial and $90\%$ fully parallelizable if you can only use $3$ processors?

$(2)$ Following the assumption of $(1),$ if the parallelized program needs to spend an additional $100$ seconds to exchange data and synchronize processors, what is the maximum speedup possible? Notice the additional $100$ seconds are charged to every processor for data exchange and synchronization in this case.

Select one of the following $4$ choices to answer $(1)$ and $(2)$:

$($a$)3,2($b$)3,2\mathrm{.}5($c$)2\mathrm{.}5,2($d$)2\mathrm{.}5,2\mathrm{.}5($e$)$ None of them is correct