GATE 2016 ME (ME2) – Question 61
For a metal-cutting job, cutting cost is ₹$18C/V$ and tooling cost is ₹$270C/(TV)$, where C is constant, V is cutting speed in m/min and T is tool life in min. Taylor’s equation is $VT^{0.25}=150$. The speed for minimum total cost is ______ m/min.
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Correct answer: 57.8 to 58.0
Explanation
Ignoring common factor C, total cost is18/V+270/(TV). Taylor equation VT^0.25=150 gives1/T=V⁴/150⁴. Thus cost is18/V+270V³/150⁴. Setting derivative−18/V²+810V²/150⁴=0 gives V=150/45^(1/4)=**57.9146m/min**; the second derivative is positive.