For a single$-$shift working in a particular turning operation, the cost of the labor and machine time in resetting a cutting edge is $$0\mathrm{.}50,$the cost of each throwaway insert having four cutting edges is $$2\mathrm{.}00,$and the depreciation of the insert holder per insert is $$0\mathrm{.}08.$The initial cost of the lathe was $$30,000,$which is amortized for $5$years$.$ Machine running costs including labor and overhead but neglecting depreciation are estimated at $$15\mathrm{.}00/$h$.$If the Taylor tool$-$life index for the carbide inserts is $0\mathrm{.}25,$calculate$,$ for minimum$-$cost conditions, the tool life, in seconds $($s$),$and cutting speed, in meters per second $($m$/$s$),$if the machine is to be used on a: a$.$Single$-$shift, $40$hr$/$wk basis

b$.$Double$-$shift, $80$hr$/$wk basis

Assuming $50$working weeks per year, a cutting speed of $7\mathrm{.}6$m$/$s$,$for $60$s tool life and a nonproductive time for loading and unloading a component of $3$mm$.$