North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of $56,000$ units

from Southernstar Exploration Company for $$60$ per unit. North Platt can manufacture the shaft at $$30$ per unit. Southernstar desires

the diameter of the shaft to be $1\mathrm{.}281cm.$ The diameter of the shaft must not be less than $1\mathrm{.}256cm$ 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 $1\mathrm{.}306cm.$ 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 $$50.$ Shown below are the diameters from a sample

of $80$ shafts manufactured during a trial run:

Required:

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

The expected loss $($total quality cost$)$ per unit, $E[(x)],$ from this process. $($Do not round intermediate calculations. Round your

answer to $2$ decimal places.$)$

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.$)$