Problem $5$

In a production turning operation, the work part diameter $=102mm$ and length $=400mm$ long. A feed of $0\mathrm{.}26m\frac{m}{r}ev$ is used in the operation. If cutting speed $=3\mathrm{.}0\frac{m}{s},$ the tool must be changed every $5$ work parts; but if cutting speed $=2\mathrm{.}0\frac{m}{s},$ the tool can be used to produce $22$ pieces between tool changes. Determine the Taylor Tool Life equation for this job.