Assuming a program consists of $50\%$ non$-$parallelizable code.

$($a$)$ Compute the speed$-$up when using $4$ processors with fixed workload size.

$($b$)$ Now assume that the parallel workload size is fixed equally per processor. Compute the speed$-$up when using $4$ processors.

$($c$)$ Explain why the speed$-$up in case $($b$)$ more than the speed$-$up in case $($a$)$