The machining time in a particular turning operation is $200$ s$,$ and the tool requires changing every five components. The nonproductive time $($loading and unloading$)$ is $300$ s per component, and the tool changing time is $150$ s$.$ The cutting speed is $2\mathrm{.}5$ m$/$s$,$ and the tool is a brazed$-$ type carbide $($n $=0\mathrm{.}25)$ that requires an expenditure of $$10\mathrm{.}00$ for regrinding $($including depreciation$).$

What should the cutting speed be changed to in order to operate at minimum cost? $($Assume a machine depreciation rate of $$10$ per hour, operator wages of $$15$ per hour, and $100\%$ overheads on operator and equipment.$)$

How much would be saved per component by operating at minimum cost?