Problem $5.$

A copper leaching operation has a stockpile with an estimated ore capacity of $0\mathrm{.}5$ million tons and an average grade of $0\mathrm{.}11\%.$ The laboratory test conducted on the ore material indicated two possible leaching conditions.

Option $1$ resulted in $67\%$ recovery of the metal with daily reagent consumption $1200g\frac{m}{?}$ ton of ore.

Option $2$ resulted in $69\%$ recovery of the metal with daily reagent consumption $1350g\frac{m}{t}on$ of ore.

Assuming leach cycle to be $180$ days for both cases, reagent cost being $$\frac{1\mathrm{.}6}{k}g$ and copper selling price to $$\frac{3\mathrm{.}5}{?}$ lbs determine; i$)$ Which option would be economical for operations to choose ii$)$ At what reagent consumption for option $2$ the mines will generate same cash flow.