Question $5(20$ points$)$

A production line has $10$ sequential workstations. Each station has a defiectrate ot o$.0\mathrm{.}4.$ An inspection$/$sortation operation occurs after every workstation to remove defective units. Each processing operation costs $\backslash (\backslash$$ $1\mathrm{.}00\backslash )$ per unit, and each inspectionlsotation operation costs $50\mathrm{.}30$ per unit.

$($a$)$ What is the total processing and inspection cost per unit for the operation as currentily defined?

$($b$)$ If the ten distributed inspections were to be replaced with one final inspection, whal would the cost per unit of this final inspection need to be$,$ to keep the total processing and inspecion cost per unit the same?