North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of $43,000$ units from Southernstar Exploration Company for $$48$ per unit. North Platt can manufacture the shaft at $$18$ per unit. Southernstar desires the diameter of the shaft to be $1\mathrm{.}289cm.$ The diameter of the shaft must not be less than $1\mathrm{.}264cm$ 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 $1\mathrm{.}314cm.$ 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 $$38.$ Shown below are the diameters from a sample of $80$ shafts manufactured during a trial run:

$\backslash$table$[[$Diameter$,\backslash$table$[[$Number of$],[$Units$]],\backslash$table$[[$Number of$],[$Diameter$]],\backslash$table$[[$Units$],[$Diameter$]],\backslash$table$[[$Number of$],[$Units$]],],[1\mathrm{.}246,1,1\mathrm{.}287,6,1\mathrm{.}306,2],[1\mathrm{.}254,2,1\mathrm{.}288,7,1\mathrm{.}307,1],[1\mathrm{.}264,3,1\mathrm{.}289,18,1\mathrm{.}308,4],[1\mathrm{.}272,2,1\mathrm{.}290,8,1\mathrm{.}312,2],[1\mathrm{.}276,2,1\mathrm{.}291,5,1\mathrm{.}314,2],[1\mathrm{.}284,3,1\mathrm{.}294,2,1\mathrm{.}318,1],[1\mathrm{.}286,6,1\mathrm{.}302,2,1\mathrm{.}334,1]]$

Required:

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

The expected loss $($total quality cost$)$ per unit, $EL(x),$ 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.$)$

$\backslash$table$[[,,,],[1.,$Expected loss,,$],[2.,$Tolerance,,$cm$