Suppose that a metal rod is supposed to be cut $51\mathrm{.}8mm.$ in length. The

upper spec limit is set at $52\mathrm{.}9mm.,$ and the lower spec limit set at $50\mathrm{.}7mm.$

A metal rod that is out of spec must be scrapped at a cost of $$40\mathrm{.}00.$ The

company uses the Taguchi Quality Loss Function to estimate quality costs.

Suppose that a sample of three units was taken, and the rod

measurements were: $52\mathrm{.}6,51\mathrm{.}8,$ and $50\mathrm{.}5mm.,$ respectively.

Harry likes the Taguchi Quality Loss function, but he believes that a linear

function would better represent the cost of quality. Specifically, Harry prefers a

loss function of the form: $L=T|D|,$ where $L,D,$ and $T$ have the same

definitions as in the Taguchi model. What would be the quality cost of the

sample of three units using Harry's model?

a$)$ The linear Taguchi parameter $T$ is $,\frac{\text{\$}}{m}m($round your response to two

decimal places$).$

b$)$ The Quality Cost of the first metal rod is $ $($round your response to two

decimal places$).$

c$)$ The Quality Cost of the second metal rod is $ $($round your response to

two decimal places$).$

d$)$ The Quality Cost of the third metal rod is $ $($round your response to two

decimal places$).$

e$)$ What is the total Taguchi$-$like Quality Cost of that sample of three units?

$ $($round your response to two decimal places$).$