The effect of cost and price fluctuations on the optimum choice of mine cutoff grades

An analytical solution to the best choice of cutoff grade for a mine is deduced for an assumed model of selective mining. It is found that this choice is determined by the constancy of a special function, the Hamiltonian, over the life of the mine. It is suggested that the appropriate constant value for this function should be determined by the expected long-term average of the paylimit. In that case, the optimum profile can be calculated at each point in time according to the prevailing working cost and product price. In particular, a decision can be made between operation at the true paylimit or at the subsidized paylimit implied by either the lease and tax formulas or the assistance formula for gold mines. It is also shown how the basic formulation can be extended for 'use in the determination of the optimum joint paylimit for two products over the life of the mine.