Problem $3.(20$ points$)$

During a turning operation, a high$-$speed steel tool is used. The price of the tool is $$55\mathrm{.}00$ and it is estimated that it can be used a

total of $20$ times before it must be scrapped. For the tool, the parameters for the Taylor equation are n$=0\mathrm{.}125$ and C$=75($m$)/($m$)$in$.$ The

standard time to grind or regrind the cutting tool is $6$ min $.$ and the grinder is paid at a rate of $$(50\mathrm{.}00)/($h$)$r$.$ The cost of operator and

machine time is $$(45\mathrm{.}00)/($h$)$r$.$ The part to be machined is $250$ mm long and $50$ mm in diameter. The time to change the tool is $4$ min $,$ the

time to load and unload the part is $5$ min $,$ and the feed is $0\mathrm{.}30$m$($m$)/($r$)$ev$.$ Calculate the following:

A$.$ Cutting speed for minimum cost

B$.$ Tool life

C$.$ Cycle time

D$.$ Cost per production unit