Optimality conditions for the continuous model of the final open pit problem

In this work we address the Final Open Pit problem in a continuous framework, that is, the problem of finding the optimal profile for an open pit that satisfies an additional slope and maximum capacity conditions on extraction. Using optimal control theory and calculus of variations tools, we provide optimality conditions for that problem. In particular, we prove that the distribution of gain along the lower border of the optimal pit must be zero, when the slope and capacity constraints are not active.