A quality characteristic understudy has a manufacturing specification $($cm$)$ of

$0\mathrm{.}2000\mathrm{.}05.$ Historical data indicates that if the quality characteristic takes on values larger than $0\mathrm{.}25$ cm or smaller than $0\mathrm{.}15$ cm$,$ the product fails and a cost of $$70$ is incurred.$$ Answer the questions below.

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a$.$ Determine the Taguchi Loss Function.

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b$.$ Estimate the loss for a quality characteristic of $0\mathrm{.}135$ cm$.$

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c$.$ If the following measurements are available for the quality characteristic x:$$

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x

$0\mathrm{.}19$

$0\mathrm{.}21$

$0\mathrm{.}25$

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d$.$ The loss function for a part is: L$($x$)=950($x$-1\mathrm{.}5)2.$ If the loss at the lower specification limit is $$30,$ determine the lower specification limit$.$