Final answer:
A 4-week cycle menu is most appropriate for a long-term care facility as it provides a good balance of variety and repetition, which is important for resident satisfaction and nutrition, in contrast to shorter cycles or static menus.
Step-by-step explanation:
For a long-term care facility, the most appropriate cycle length for planning meals using cycle menus is a 4-week cycle menu. This length of time allows for a significant variety of meals, which is important for resident satisfaction and nutrition. It prevents menu fatigue and helps cater to the diverse preferences and dietary needs of the residents. In contrast, a 2-week cycle might not offer enough variety, and a 1-week cycle would likely become repetitive very quickly. A restaurant style static menu is not typically used in long-term care facilities because it doesn't offer the necessary variety over time.