Project ForgePlant Design & Economics
Cost Estimation
GATE 2018
Hard
AFC(Rs.Lakh)=641R²−1796R+1287+1/(R−1.16) and AUC(Rs.Lakh)=80+62.5R for a distillation column, as functions of reflux ratio R. The optimum reflux ratio Ropt for minimum total cost may be found by solving
- A1282Ropt−1796−1/(Ropt−1.16)²=0
- 62.5+1282Ropt−1796−1/(Ropt−1.16)²=0
- C80+62.5Ropt+641Ropt²−1796Ropt+1287+1/(Ropt−1.16)=0
- D80+62.5Ropt−641Ropt²+1796Ropt−1287−1/(Ropt−1.16)=0
Explanation
Minimizing total cost=AFC+AUC requires d(AFC)/dR+d(AUC)/dR=0: [1282R−1796−1/(R−1.16)²]+62.5=0, i.e. 62.5+1282R−1796−1/(R−1.16)²=0.
Source: GATE CH 2018 (2018)
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