Benders Decomposition (1962) solves large mixed-integer programs by splitting them into a master problem (integer variables: which facilities to open) and a subproblem (continuous: how to route clients to open facilities). The subproblem's dual generates Benders cuts that are added back to the master, progressively tightening its objective estimate. This exploits problem structure: solving many small subproblems is often far cheaper than one giant MIP. The visualization shows the facility location problem — open/close decisions drive the master, while client assignment is delegated to the subproblem via LP duality.