Final answer:
The department that is most likely to exceed its planned hours by the end of the project is the department facing competing priorities and resource constraints.
Step-by-step explanation:
The department that is most likely to exceed its planned hours by the end of the project is the department that is facing competing priorities and resource constraints. In the given information, it is mentioned that staff members are engaged in this project while managing their other funded projects. This means that they have limited time and resources to dedicate solely to this project, increasing the likelihood of exceeding planned hours.
For example, in the case of staff burnout, as mentioned in the information, staff members may already be overburdened and under-resourced. Participating in this project can worsen their burnout and lead to a faster rate of exhaustion, causing them to exceed their planned hours for the project.
Therefore, it is important to consider the impact of competing priorities and resource constraints when determining which department is most likely to exceed its planned hours.