$[15$ points$]$ A company has a machine with $3$ control knobs $($A$-$C$).$ The president hires a consultant to run a Taguchi experiment to get the best settings for the machine. The consultant runs the experiments, shown below, with a "bigger is better" metric.

$\backslash$table$[[$Experiment$,$A$,$B$,$C$,$Output $($db$)],[1,1,1,1,11\mathrm{.}4],[2,1,2,2,14\mathrm{.}3],[3,2,1,2,12\mathrm{.}9],[4,2,2,1,8\mathrm{.}7]]$

a$)[8$ points$]$ Determine the best machine setting using the Taguchi method.

b$)[7$ points$]$ Compute the expected machine output for the setting found in part a$.$