We develop the rectangular choice-of-technology model with factor constraints, or RCOT, a linear programming input-output model for analysis of the economy of a single region. It allows for one or more sectors to operate more than one technology simultaneously, with the relatively lowest-cost one supplemented by others if it encounters a binding factor constraint. The RCOT model solves for sector outputs, goods prices that are set by the highest-cost technologies in use, and scarcity rents that correspond to binding factor constraints experienced by the lower-cost technologies. The model is motivated by the fact that mineral deposits of different qualities may be exploited simultaneously, as may primary and recycled sources for the same materials or irrigated and rainfed techniques for producing the same crop. RCOT generalizes Carter’s square choice-of-technology model, in particular adding the factor constraints that allow several alternatives to operate simultaneously. The Appendix gives a numerical example.