Project ForgePlant Design & Economics
Cost Estimation
GATE 2017
Hard
The total cost of an equipment is CT=2x+12000/(xy)+y+5. The optimal value of CT, rounded to 1 decimal place, is
91.5(± 2 accepted)
Explanation
Setting ∂CT/∂x=0 and ∂CT/∂y=0 gives x²y=6000 and xy²=12000, so x=0.5y. Substituting: 0.5y³=12000 ⟹ y≈28.84, x≈14.42. CT=2(14.42)+12000/(14.42×28.84)+28.84+5≈91.5.
Source: GATE CH 2017 (2017)
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