Solved at Scale
Solved with CP-SAT
An external CP-SAT solver solves the pinned five-variable instance under deterministic parameters and proves the optimum. The lesson quotes only the deterministic fields of the run, and the values shown are decoded from the run's own solution values.
Invocation
The invocation is cpsat_stream_solve solve mip_var_array.jsonl --params num_search_workers:1,random_seed:1, with the solution values written to a temporary --sol file. Why: a single search worker and a fixed seed make the run deterministic, so the solution quoted below is reproducible rather than anecdotal.
Solver result
The solver reports status OPTIMAL with objective value 260 and best objective bound 260. Why: OPTIMAL means the solver proved a matching bound, not merely found a good solution. The output also carries timing, conflict, and branch counts; those fields are omitted here because they vary from run to run, and only the status, the objective value, the bound, and the solution values are deterministic.
The decoded values
x1 is 10, x2 is 16, x3 is 4, x4 is 4, and x5 is 3. Why: these are the literal decoded solution values from the real solve, and the labels x1 through x5 are the diagram's own column labels. The model file itself carries a solution hint equal to this exact point — an honest detail, not a hidden one: this instance has more than one optimal solution, and the hint is what steers the solver to this particular one rather than a different optimum with the same objective value.
Diagram note
The table has one column per variable, x1 through x5, and one row carrying each decoded value; the caption's objective is recomputed from those values on every build. Pixel positions are rounded for layout; every number shown is exact.