$20$Intheproductionofapartforaprinter,foursequentialoperationsareinvolved.Unitprocessingcostsfortheoperationsare$$10,$$$6,$$$15,$and$$20,$respectively.Thefirst$-$passyieldsforeachoperationare$0\mathrm{.}95,0\mathrm{.}90,0\mathrm{.}95,$and$0\mathrm{.}85,$respectively.Unitinspectioncostsaftereachoperationare$$0\mathrm{.}50,$$$2\mathrm{.}00,$$$3\mathrm{.}00,$and$$5\mathrm{.}00,$respectively.

$($a$)$

Ifnoinspectionisperformed,whatistheunitcostforanacceptablepart?

$($b$)$

Assumethataninspectionprocessisabletoidentifyallpartscorrectly.Supposethatinspectionisconductedonlyafterthefirstandsecondoperations.Nonconformingpartsarenotforwardedtothenextoperation.Whatistheunitcostperacceptablepart?

$($c$)$

Supposethatinspectionisconductedonlyafterthethirdoperation.Nonconformingpartsarenotforwardedtothenextoperation.Whatistheunitcostperacceptablepart?

$($d$)$

Basedontheunitcostscomputedinparts$($b$)$and$($c$),$discusswhere,ingeneral,inspectionsshouldbeconducted.