$($d$)$ A $3-$stage pipeline was designed with its individual stages taking $\backslash (0\mathrm{.}1,0\mathrm{.}2\backslash )$ and $0\mathrm{.}3$ ms to complete respectively. Assume that the same function can be carried out in $0\mathrm{.}5$ ms without using a pipelining design.

$(1)$ What is the speedup ratio if the pipeline carries out $100$ processes? Note that the speedup ratio is the ratio of the time taken without using the pipeline design to the time taken with the pipeline design.

$(4$ marks$)$

$(2)$ What is the maximum speedup ratio?

$(2$ marks$)$