You work as a full-time project manager working within the customer operations organization, reporting to the VP of customer solutions. Your supervisor manages the project budget. Which organizational structure do you join in?

The question describes a hybrid organizational type, likely a mixture of a weak and a strong matrix. A clue is that your title is project manager, which does not typically exist in a purely functional organization; another is that the functional manager manages the project budget, which is not typical in a project-oriented or PMO organizational type.