Project ForgePlant Design & Economics
Profitability Analysis
GATE 2010
Hard
For the same phenol plant (variable cost 45,000+5P Rs/tonne, fixed charges Rs. 100,000/day, selling price Rs. 50,000/tonne), the break-even capacity in tonnes per day, is
- A50
- B40
- C30
- 20
Explanation
Revenue=Cost: 50000P=100000+P(45000+5P) ⟹ 5000P−100000−5P²=0 ⟹ P²−1000P+20000=0 ⟹ P=[1000±√(1000000−80000)]/2=[1000±959.2]/2. The lower (break-even) root is P≈20.4≈20.
Source: GATE CH 2010 (2010)
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