A $3$ in diameter, $12$ in long cylindrical workpiece is to be turned down to $2\mathrm{.}8$ in in

two identical passes on a CNC turning machine using feed f $=0\mathrm{.}005$ in$/$rev$.$ The cut will be

made with a tool whose Taylor tool life parameters are n $=0\mathrm{.}25$ and C $=1100$ ft$/$min$.$ The

machine is semiautomatic; so an operator loads and unloads the machine; the total handling time

$($loading and unloading$)$ of a part is $3$ min. and the tool change time is $2$ min. The machine takes

$0\mathrm{.}8$ min in total to position the tool for the two passes together. The cost of the operator and

machine $=$ $$42/$hr$,$ the machine uses $3-$cutting$-$edge cemented carbide inserters; the cost of one

insert is $9$ $$.$ Determine $($a$)$ the time to complete one production cycle at minimum cost, $($b$)$ cost

of the production cycle. $($c$)$ If the setup time for this job is $4\mathrm{.}0$ hours and the batch size $=320$

parts, how much will it cost to complete one batch?