North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of $50,000$ units from Southernstar Exploration Company for $$80$ per unit. North Platt can manufacture the shaft at $$50$ per unit. Southernstar desires the diameter of the shaft to be $1\mathrm{.}275$ cm$.$ The diameter of the shaft must not be less than $1\mathrm{.}25$ cm in order to fit properly inside the sleeve. To be able to insert the shaft into a sleeve without the use of force, the diameter cannot be larger than $1\mathrm{.}30$ cm$.$ A defective shaft is discarded and a replacement has to be shipped via express freight to locations around the world. North Platt estimates that the average cost of handling and shipping a replacement shaft will be approximately $$70.$ Shown below are the diameters from a sample of $80$ shafts manufactured during a trial run:

Diameter Number of Units Diameter Number of Units Diameter Number of Units

$1\mathrm{.}23211\mathrm{.}27361\mathrm{.}2922$

$1\mathrm{.}24021\mathrm{.}27471\mathrm{.}2931$

$1\mathrm{.}25031\mathrm{.}275181\mathrm{.}2944$

$1\mathrm{.}25821\mathrm{.}27681\mathrm{.}2982$

$1\mathrm{.}26221\mathrm{.}27751\mathrm{.}3002$

$1\mathrm{.}27031\mathrm{.}28021\mathrm{.}3041$

$1\mathrm{.}27261\mathrm{.}28821\mathrm{.}3201$

Required:

Set up an Excel spreadsheet that uses a Taguchi quality loss function to determine:

$1.$ The expected loss $($total quality cost$)$ per unit, E$[$L$($x$)],$ from this process. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

$2.$ The diameter tolerance that should be set for the manufacture of the shaft. $($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$