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Derive an expression for optimum cutting speed and tool life for both minimum production cost and maximum production rate during machining process.
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Calculation of different Cost elements:

Let ; D= Diameter of job in mm

L= length of the job in mm

f=feed in mm/rev

N= rotational speed.=$\frac{1000 V}{π ×D}$

$t_m$ =machining speed of work piece. =$\frac{L}{f ×N}$

$t_h$= handling or loading time.

$K_1$= Operating cost.

$t_c$= tool changing time for one …

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