A mathematical model can minimize the total cost of rock mass excavation. The total excavation cost model consists of functions defining the owning and operating costs for a drill, explosive and auxiliary explosive loading equipment, and an excavating machine. These functions contain variables that describe certain remotely sensed physical features of both the pre-blasted rock mass volume and the fragments that result from blasting. Remote sensing was performed within operating open pit Gold and Copper mines located within the Western United States. For a remotely sensed rock mass, the model automatically determines the rock mass volume and the explosive mass that result in minimum total excavation cost. The model estimated minimum total excavation cost for different loading machines over a range of rock mass conditions that are characteristic of those observed within the mines. The results suggest that a model including the cost of a comminutive process for minimizing the cost of reducing the size of rock mass is feasible.