A research institute is running large$-$scale weather simulations using a high$-$performance

computing system. The simulations involve a variety of tasks, such as data assimilation,

atmospheric model computation, and visualization.

$($a$)$ The execution of a scientific simulation program involves TWO $(2)$ main stages: data

preprocessing and computation. To optimize the program's performance, you, as the

system developer, have parallelized the computation stage, achieving a speedup to $75\%$

in that portion of the program $.$ However, the preprocessing stage remains sequential at

$25\%,$ and its execution time has not improved.

Identify the problems that occurred during the adoption of parallel computing to the

system that lead to the suboptimal performance with four processing elements $($N$=4).$

Calculate the max imum possible improvement in a system's performance and suggest

THREE $(3)$ solutions to overcome the problem.

$[12$ marks$]$