In certain machining operation with a cutting speed of $$50$$ $$m/min,$$ tool life of $$45$$ minutes was observed, when the cutting speed was increased to $$100$$ $$m/min,$$ the tool life decreased to $$10$$ minutes. The cutting speed for maximum productivity, if tool change time is $$2$$ minutes is

Tool life in drilling steel using $$HSS$$ drill is expressed as $${T^{0.2}} = 9.8\,\,{D^{0.4}}\,\,/\,\,V\,{s^{0.5}}$$ where $$D$$ is the drill diameter (in $$mm$$), $$T$$ is the tool life (in minutes), $$V$$ is the cutting speed (in $$m/min$$) and $$s$$ is the feed ($$mm/rev$$). The feed is set at maximum possible value of $$0.4$$ $$mm/rev$$ for a given drill diameter of $$30mm.$$ The length of drilling is $$50mm.$$ The machine hour rate Rs $$60$$ and the cost of drill is Rs. $$400.$$

$$i)$$ For the given conditions, the tailor's exponent and constant are .............
$$ii)$$ The optimum cutting speed, $${V_{opt}},$$ neglecting the work-piece and tool changing times is

In Whitworth quick return mechanism (used in shapers) the velocity of the $$ram$$ is maximum at

For $$50\% $$ penetration of work material, a punch with single shear equal to thickness will