Open pit mines contain ore to be extracted from the surface downwards to obtain a profit. This is achieved using large pieces of equipment with significant space requirements to extract the material from the surface. Unfortunately, the industry currently lacks a standard methodology for optimizing the designs of these spaces; current practice may lead to inconsistent, subjective and suboptimal results. Automatic design of practicable portions of the mines called pushbacks is a desirable tool for the mining industry. This article proposes a new approach based on an integer linear programming model (ILP) determining the volumes to be extracted to maximize profit while respecting geospatial and design constraints. Design constraints require that the minimum width be respected at the bottom of the mine and between successive pushbacks. The ILP is applied to three case studies to show that the model can generate practical solutions in minutes.