batch of $200$ parts is to be produced on a CNC tuming machine, each part in the batch has $3$ in diameter and length of $10$ in$.$ Each part is to be turned down to $2\mathrm{.}88$ in in identical several passes using same cutting conditions. The machine uses feed $=0\mathrm{.}005$ in$/$rev and depth of cut $=0\mathrm{.}02$ in$,$ and a cutting tool having a Taylor tool life parameters n $=0\mathrm{.}24$ and C $=1000$ ft$/$min$.$ An operator loads and unloads the machine; the total handling time $($loading and unloading$)$ of a part is $2\mathrm{.}8$ min. and the tool change time is $2\mathrm{.}3$ min. The machine takes $0\mathrm{.}3$ min to position the tool for each pass. The cost of the operator and machine $=$ $$40/$hr$,$ the machine uses $4-$cutting$-$edge cemented carbide inserters; the cost of one insert is $12$ S$.$ Determine: $($a$)$ Number of passes $($b$)$ The time to complete one production cycle at minimum cost $($c$)$ Cost of the production cycle.