In the context of project management, when a team member encounters an issue such as a non-working computer, it is essential for the project manager to take a proactive approach to resolve the issue promptly.
This is to ensure that the project work is not delayed and the team member can continue contributing to the project. According to the PMBOK guide, the project manager should facilitate problem-solving and provide support to team members to address and resolve issues that can impact project progress1.
References:
PMBOK Guide - Seventh Edition1
PMP Examination Content Outline - June 20192
Professional in Business Analysis Reference Materials3

When a project sponsor requests an additional deliverable, especially when the project is significantly underway, the first action a project manager should take is to determine the potential impact of this change on all aspects of the project. This involves assessing how the new deliverable will affect the project's scope, time, cost, quality, resources, and risks. The project manager needs to analyze whether the additional deliverable aligns with the project objectives and how it might alter the project plan. This impact analysis is crucial before moving forward with any decisions or negotiations related to the change request.
: The response is aligned with the principles outlined in the PMBOK Guide's "Perform Integrated Change Control" process, which emphasizes the importance of assessing the impact of change requests as a first step1. Additionally, the role of Business Analysts in evaluating the impact of proposed changes on various aspects of the organization is highlighted, which supports the necessity of impact assessment in change management2.

According to the PMBOK Guide, the project manager is responsible for managing the communication among stakeholders, and ensuring that the information needs of the project are met (Section 10.1). The project manager should also establish and enforce the ground rules for communication within the project team, and address any issues that may arise from unauthorized or inappropriate communication (Section 9.3.2.4). By pointing out to the project team and the customer that all information concerning the timeline of the project should be communicated by the project manager, the project manager can prevent confusion, misunderstanding, and conflict among the stakeholders, and maintain control over the project scope and schedule. This is also consistent with the Professional in Business Analysis (PMI-PBA) Examination Content Outline, which states that one of the tasks of a business analyst is to "communicate requirements information to stakeholders according to the communication plan" (Task 4.3). References:
* PMBOK Guide, 6th Edition, Section 10.1, Section 9.3.2.4
* Professional in Business Analysis (PMI-PBA) Examination Content Outline, Task 4.3

When faced with a lack of responsiveness from a vendor, it is crucial for the project manager to address the issue directly and proactively. Inviting the vendor to a meeting allows for open communication and the opportunity to discuss and resolve the concerns. This approach aligns with best practices in vendor management and stakeholder engagement, which emphasize the importance of clear and purposeful communication, especially when issues arise that could impact project delivery. By discussing the concerns, the project manager and vendor can collaboratively identify the root causes of the lack of responsiveness and work towards a solution that ensures the project's success.
References: The answer is supported by best practices in vendor management, which suggest that direct communication is key to resolving issues and maintaining a successful partnership. The approach of inviting the vendor to a meeting is consistent with the principles outlined in the PMBOK Guide, which advocates for proactive stakeholder engagement and communication12. Additionally, the Professional in Business Analysis (PMI-PBA) materials highlight the importance of vendor analysis and relationship management as part of business analysis activities345.