Modeling optimal exploration and extraction of mineral resource

With consideration of the mineral resource owner's attempt to maximize his benefits from the total resources, this paper puts forward a dynamic model on the optimal exploration and extraction rates of resources. The paper points out that the optimal exploration and extraction rates calculating model is as same as the maximum benefits calculating model. The necessary conditions for the maximum benefits or the optimal rates of exploration & extraction are discussed. The optimal rates of exploration and extraction at any different time are presented.