The project manager should analyze both projects to determine the most effective use of common resources, such as human, material, equipment, or facilities1. This will help the project manager to allocate and balance the resources across the two projects, and to identify and resolve any resource conflicts or shortages2. This may also help to reduce the duration of the critical project by ensuring that the required resources are available when needed. The other options are not appropriate or feasible in this situation. Applying fast-tracking techniques to compress the schedule of the critical project is not possible, as the question states that the schedule does not have activities that can be overlapped3. Using resource optimization to justify requesting more resources for the critical project may not be realistic, as the question implies that the project manager does not have access to additional resources4. Providing schedule optimization training to the project teams to improve their skills may not have an immediate impact on the duration of the critical project, and may also consume more time and resources. References: 1: PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Seventh Edition, Project Management Institute Inc., 2021, p. 201. 2: PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Seventh Edition, Project Management Institute Inc., 2021, p. 202. 3: PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Seventh Edition, Project Management Institute Inc., 2021, p. 211. 4: PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Seventh Edition, Project Management Institute Inc., 2021, p. 203. : PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Seventh Edition, Project Management Institute Inc., 2021, p. 212.