For a certain job, the cost of metal cutting is Rs 18 C/V and the cost of tooling is Rs 270C(TV), where C is a constant, V is the cutting speed in m/min and T is the tool life in minutes. The Taylor's tool life equation is $V T^{0.25} = 150$ , The cutting speed (in m/min) for the minimum total cost is
57.91

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Solution

The correct option is A 57.91
Total cost = metal cutting cost + tooling cost
$= \frac{18 C}{V} + \frac{270 C}{V T}$

Here, $T = {(\frac{150}{V})}^{\frac{1}{0.25}} = {(\frac{15}{V})}^{4}$

$C_{1} = \frac{18 C}{d V} = 0$

$\frac{d C_{1}}{d V} = 0$

$- \frac{18 C}{V^{2}} + \frac{270 C}{{(150)}^{4}} \times 3 v^{2} = 0$

$o r V^{4} = \frac{150^{4} \times 18}{270 \times 3}$

$V = 57.91 m / min$

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