$1-$ The part on the right is obtained after turning the part on the left. The following parameters are the maximum parameters that can be used for this process on the lathe: Feed rate $0\mathrm{.}25m\frac{m}{r}ev$; Depth of cut: $2$ mm ; Rotational speed $4000$ rpm $.$ For the given process a$)$ Determine the minimum machining time$($ sec $).$ b$)$ Determine the maximum and minimum cutting speed $(\frac{m}{m}in)$ c$)$ Determine the maximum $MRR(m\frac{m^3}{m}in)[25$ Pts$].$

Please answer all parts step by step with the relevant equations $?$