Many print-heads today consist of multiple nozzles. Hardware limitations and print quality requirements make it difficult to print from all nozzles or even adjacent nozzles at a given time. Print modes are established to trade-off between print speed and print quality requirements based on different media, ink, and image content. A print mask associates each pixel of the image with a pass number for a given print mode. Given a printing system, this study formulates a constrained optimization problem to generate all admissible print masks that maximize throughput (i.e. minimizes the number of passes) subject to constraints reflecting hardware limitations and print quality requirements. Two examples will be given to show the utility of these methods.