Consider four system configurations involving demand paging.

In system S$1,$ the main memory size is $1$ GB with a cost of $$100.$ The memory access time $($i$.$e$.,$ when a page is accessed without a page fault$)$ is $0\mathrm{.}1$ ms$.$ The disk drive in this system configuration costs $$75$ and the page fault service time $($i$.$e$.,$ the average time to identify a page to replace, write it out if needed, and bring in the new page from disk$)$ is $2$ ms$.$

In system S$2,$ the main memory size is $0\mathrm{.}5$ GB and its cost is $$75.$ The memory access time is $0\mathrm{.}075$ ms$.$ The disk drive costs $$125$ and the page fault service time is $1\mathrm{.}5$ ms$.$

In system S$3,$ the main memory size is $2$ GB and its cost is $$125.$ The memory access time is $0\mathrm{.}1$ ms$.$ The disk drive costs $$125$ and the page fault service time is $1\mathrm{.}5$ ms$.$

In system S$4,$ the main memory size is $2$ GB and its cost is $$100.$ The memory access time is $0\mathrm{.}2$ ms$.$ The disk drive costs $$125$ and the page fault service time is $1$ ms$.$

Let the page fault rate in the four systems be $10\%,15\%,7\mathrm{.}5\%$ and $7\mathrm{.}5\%$ respectively.

Determine the performance, in terms of the effective memory access time $($i$.$e$.,$ the time it takes on average to access a page in memory$),$ for the four system configurations S$1,$ S$2,$ S$3,$ S$4.$ Identify the TRUE statement from the following choices regarding the price$-$performance ratios of the four systems $($note that in this context, system A will have a better price$-$performance ratio if the product of its total cost of main memory as well as disk drive and its effective memory access time is smaller than the corresponding value for system B$)?$

Question $5$ options:

S$2$ has the worst price$-$performance ratio.

S$3$ has the best price$-$performance ratio.

S$4$ has better price$-$performance ratio than S$3.$

S$1$ has the best price$-$performance ratio.