Final answer:
The organizational structure that combines departmentalization by division and function for dual benefits is the Matrix structure.
Step-by-step explanation:
The kind of structure that combines departmentalization by division or program and function to gain the benefits of both is known as the Matrix structure. In a matrix organization, the vertical hierarchy is complemented by a horizontal structure that promotes collaboration, thereby enabling quick response to changes in the environment and leveraging diverse skills within teams. This contrasts with older, more rigid organizational structures that are purely hierarchical and can obstruct value-adding activities due to the creation of silos. The matrix structure adheres to the principle that 'form follows function,' integrating both specialized and shared functions to increase efficiency, and is used by companies to maintain agility and leverage expertise across different organizational dimensions.