Solved at Scale
A Bigger Integer Program
Five general-integer variables with their own domains and four constraint rows form the real instance the external solver reads, parsed from its model file. At five variables the relaxation picture no longer exists, so the table replaces the picture.
The instance
There are 5 integer variables, x1 through x5, and 4 constraint rows, all parsed from the solver's model file at build time, not hand-typed. Why: the variables are general integers with their own upper bounds — x1 up to 50, x4 up to 125 — not booleans and not one shared domain.
No drawable picture
The earlier chapters' instances had 2 variables, so the relaxation polytope and the branch-and-bound tree are literally drawable; at five variables no polytope picture exists and the table replaces the picture. Why: the domain grid alone holds 1625829408 integer points — far beyond anything drawn by hand.
The objective
The model maximizes 7 times x1 plus 8 times x2 plus 2 times x3 plus 9 times x4 plus 6 times x5, and some constraint coefficients are negative — the row tables show them plainly. Why: this lesson only presents the instance; solving, with its certificate, comes next.
Diagram note
The first table lists the four constraint rows, row_0 through row_3 — the model's own constraint names — with their bound column; the second lists the objective row and the per-variable domain row. Pixel positions are rounded for layout; every number shown is exact.