Optimum printing resolution depends on the process they are using. Best to ask them. It can vary greatly depending on their equipment. They will probably state a number that is DPI (dots per inch) instead of pixels. But basically they are interchangeable for your calculation. For instance, if they state 300 dpi and your image is 4000 pixels wide, then divide 4000 by 300 and that is the optimum width of the printed piece. (4000 pixels/300 dpi = 13.3 inches).