Final answer:
The type of manufacturing system described is a flexible manufacturing system (FMS), which utilizes computer control and automation to efficiently produce a variety of products.
Step-by-step explanation:
The type of computer-assisted manufacturing system that is capable of producing a family of products from start to finish using robots and other automated equipment under the control of a mainframe computer is known as a flexible manufacturing system (FMS). This system allows for a greater adaptation to changing production needs compared to more traditional manufacturing approaches, and typically incorporates technologies that enable a range of different products to be produced with minimal manual intervention. Choices in production technology, as with FMS, present firms with options for combining labor and physical capital to maximize efficiency and profits by reducing production costs.