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We aim to obtain by viscosity solution method the closed-form solution of a model concerning natural resource extraction in which a firm draws a schedule of when to stop the extraction. In this model, a regime-switching stochastic process is introduced to simulate the price of some natural resource. To solve the model, we first develop a theory, as a part of the results in the paper, that also applies to other optimal stopping problems containing regime-switching ingredients. Then using the theory, we solve the model completely and rigorously. A numerical example is given to display the results of the model.