Question

The relevant information on metal extraction from a copper mine are given below: Selling price of copper (Rs./kg) = 900
Mining cost (Rs./tonne of ore) = 500
Processing cost (Rs./tonne of ore) = 2000
Overall recovery of copper metal (%) = 70
Ignoring all other costs, the breakeven cutoff grade of copper, in %, is:

Hint:

To find the breakeven cutoff grade: \[ {Cutoff grade} = \frac{{Total cost}}{1000 \times {Recovery} \times {Selling price}} \] Express your answer as a percentage.

Answer 1

Step 1: Understanding the breakeven cutoff grade. At breakeven, the revenue from recovered copper = total cost of mining and processing: \[ {Revenue} = {Grade} \times 1000 \times {Recovery} \times {Price} \] \[ {Cost} = {Mining cost} + {Processing cost}. \] Let cutoff grade be \( G \) (in decimal form). 
Step 2: Write the breakeven equation. \[ G \times 1000 \times 0.70 \times 900 = 500 + 2000. \] \[ G \times 1000 \times 630 = 2500. \] \[ G = \frac{2500}{630000} = 0.003968. \] Step 3: Convert to percentage and round off. \[ G = 0.3968% \approx \boxed{0.40%}. \]