Q$5.$ A processing sequence consists of $16$ operations, each of which is followed by an inspection

and sortation operation to detect and remove defects generated in the processing operation.

Defects in each process occur at a rate of q $=0\mathrm{.}02.$ Each processing operation costs $$2\mathrm{.}50$ per

unit processed, and the inspection$/$sortation operation costs $$0\mathrm{.}15$ per unit. Batch size is $25,000.$

$($a$)$ Determine the total processing and inspection costs for this distributed inspection system. $($b$)$

A proposal is being considered to combine all of the inspections into one final inspection and

sortation station following the last processing operation. Determine the cost per unit of this final

inspection and sortation station that would make the total cost of this system equal to that of the

distributed inspection system.