$(25$ pts$)$ Assume that you are considering enhancing a machine by adding a special feature to it$.$ The percentage of time $($the original run time before the feature is added$)$ that the machine can be run using this new feature is denote as $p\%,$ and, during this portion of time, the machine with this new feature runs $f\%$ faster than the old one without it$.$

$($a$)$ Determine the overall speedup for each of the following:

i$.p=80,f=40$

ii$.p=50,f=80$

iii. $p=30,f=100$

iv$.p=10,f=200$

$($b$)$ Draw a graph that plots together each of the two speedup functions for $f=100$ and $f=300$ in terms of $p$ with $p$ ranging from $0$ to $100(y-$axis being the speedup and $x-$axis being $p).$