It has been determined that Taguchi's Loss Function constant for a part is $k=$$$\frac{8}{m}{m}^2.$ The process

target is $m=4\mathrm{.}2mm$ and the process has been running with $=4\mathrm{.}4mm$ and $=0\mathrm{.}12mm.$

a$.$ Find the average loss per part under the conditions described.

b$.$ Find the average loss per part after the process is centered.

c$.$ Find the average loss per part after the process is centered and the process variation is cut in half.