The optimal management of a non-renewable resource extraction project is studied when input and output prices follow correlated stochastic processes. The decision problem is specified by two Bellman equations describing the project when it is currently operating or mothballed. Solutions are determined numerically using the Least Squares Monte Carlo methodology. The analysis is applied to an oil sands project which uses natural gas during extracting and upgrading. The paper takes into account the co-movement between crude oil and natural gas prices and proposes two price models: one incorporates a long-run link between the two while the other has no such link. Incorporating a long-run relationship between oil and natural gas prices has a significant effect on the value of the project and its optimal operation and reduces the sensitivity of the project to the natural gas price process.