We consider a real options model for the optimal irreversible investment problem of a
profit maximizing company. The company has the opportunity to invest into a production plant
capable of producing two products, of which the prices follow two independent geometric Brownian
motions. After paying a constant sunk investment cost, the company sells the products on the market
and thus receives a continuous stochastic revenue-flow. This investment problem is set as a twodimensional
optimal stopping problem. We find that the optimal investment decision is triggered by a
convex curve, which we characterize as the unique continuous solution to a nonlinear integral equation.
Furthermore, we provide analytical and numerical comparative statics results of the dependency of
the project's value and investment decision with respect to the model's parameters.