North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of $57,000$ units from Southernstar Exploration Company for $$160$ per unit. North Platt can manufacture the shaft at $$130$ per unit. Southernstar desires the diameter of the shaft to be $1\mathrm{.}282$ cm$.$ The diameter of the shaft must not be less than $1\mathrm{.}257$ 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 $1\mathrm{.}307$ 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 $$150.$ Shown below are the diameters from a sample of $100$ shafts manufactured during a trial run:

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

$1\mathrm{.}23921\mathrm{.}28071\mathrm{.}2993$

$1\mathrm{.}24731\mathrm{.}28181\mathrm{.}3002$

$1\mathrm{.}25741\mathrm{.}282231\mathrm{.}3016$

$1\mathrm{.}26531\mathrm{.}28391\mathrm{.}3052$

$1\mathrm{.}26931\mathrm{.}28441\mathrm{.}3072$

$1\mathrm{.}27741\mathrm{.}28731\mathrm{.}3111$

$1\mathrm{.}27971\mathrm{.}29531\mathrm{.}3271$

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.$)$