Consider a gold mine with two processing facilities: a leach plant and a mill. For the\ leach plant and the mill, the processing cost is $2.00 and $12.00 per tonne, respectively.\ The gold price is $270.00 per ounce from which must be deducted a $5.00 per ounce\ charge.\ a) Plot utility functions for leached and milled material if we assume a constant 60%\ and 90% recoveries for leached and milled material respectively.\ b) What is the leach-mill cut-off grade (grams/tonne) for part a.\ c) The figure below shows relationship between recoveries and average grade. Plot\ utility functions for leached and milled material.\ d) What is the leach-mill cut-off grade (grams/tonne) for part c.\ (1 oz = 31.1035 g)\ Q2) Consider a copper mining operation where material is being milled. The cost\ associated with this operation are as follows:\ Percentage of copper recovered 87%\ Price of copper $1.20 / pound of copper sold\ Freight, smelting, and refining costs $0.30 / pound of copper sold\ Ore mining cost $1.00 / tonne of ore processed\ Ore processing cost $3.00 / tonne of ore processed\ Ore overhead cost $0.50 / tonne of ore processed\ Waste mining cost $1.00 / tonne of waste mined\ Environmental control and remediation cost $0.05 / tonne of waste mined\ Waste overhead cost $0.05 / tonne of waste mined\ (1 tonne = 2205 lbs)