Project ForgePlant Design & Economics
Profitability Analysis
GATE 2010
Hard
A plant produces phenol. The variable cost in rupees per tonne of phenol is related to the plant capacity P (in tonnes/day) as 45,000+5P. The fixed charges are Rs. 100,000 per day. The selling price of phenol is Rs. 50,000 per tonne. The optimal plant capacity (in tonnes per day) for minimum cost per tonne of phenol, is
- A101
- 141
- C283
- D422
Explanation
Cost per tonne C(P)=[100000+P(45000+5P)]/P=100000/P+45000+5P. dC/dP=−100000/P²+5=0 ⟹ P²=20000 ⟹ P=√20000≈141.4.
Source: GATE CH 2010 (2010)
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