Problem $3[24$ pts$]$: Three Stooges

Moe, Larry and Curly have just purchased three new computers, each with its own processing speed and sorting algorithm:

where $\backslash ($ T$($n$)\backslash )$ is the number of comparisons it takes, in the worst case, to sort a list of size $\backslash ($ n $\backslash ).$

Note that questions ii and iii below are not easily solved with pencil and paper, please show an initial equation and use Wolfram Alpha $($https:$//$www$.$wolframalpha.com$/$ input? $\backslash (=$x $\backslash \%5\backslash$mathrm$\{$E$\}2+\backslash \%2\backslash$mathrm$\{$~B$\}+5\backslash$mathrm$\{$x$\}+\backslash \%2\backslash$mathrm$\{$~B$\}+6+\backslash \%3\backslash$mathrm$\{$D$\}+17+\backslash$mathrm$\{$x$\}\backslash ))$ to compute a final answer $($the "solutions" box on the linked page may be helpful$).$ There is a very similar example in recitation$10,$ whose solutions you may access, which may also be helpful here.

i What is the smallest list input size $\backslash ($ n $\backslash )($whole number$)$ which ensures that, for any larger $\backslash ($ n $\backslash )$ and worst case list per method, Larry's computer sorts faster than Moe's?

ii What is the smallest list input size $\backslash ($ n $\backslash )($whole number$)$ which ensures that, for any larger $\backslash ($ n $\backslash )$ and worst case list per method, Curly's computer sorts faster than Moe's?

iii What is the smallest list input size $\backslash ($ n $\backslash )($whole number$)$ which ensures that, for any larger $\backslash ($ n $\backslash )$ and worst case list per method, Curly's computer sorts faster than Larry's?