A computer simulation is observed to take $21$ hours to execute on a PC with one dual$-$core processor,

and is estimated to have a parallel fraction of $95\%.$ It is proposed to purchase a computer with $2$x $8-$

core processors, or to lease a cloud$-$based computing resource with $64$ cores $($in each case assume they

are of similar architecture$).$

Calculate the following $($times can be calculated to the nearest hour$)$:

$($i$)$ The compute time $($for a single core$).$

$($ii$)$ The speedup and wallclock time for each of the proposed solutions.

$($iii$)$ If the problem is made $20$ times larger, give a best$-$case estimate of the speedup, and

wallclock time, for this larger problem on the two proposed options.

$(6$ marks$)$