Building the Dual

The Dual of the Flagship

The flagship problem from the first two books has a concrete dual. This lesson builds that dual directly from the primal coefficients and right sides. The result is the certificate problem that will bound the primal maximum.

highlighted = computed this step

Dual objective

The flagship dual minimizes 4y1 plus 4y2. Why: the primal right sides become dual objective weights.

min⁡ 4y1+4y2\min\ 4y_{1}+{}4y_{2}
Flagship dualThe concrete dual is recomputed from the flagship primal.dual objective44dual constraints211121

Dual constraints

The first dual constraint has coefficients 2 and 1 with right side 1. Why: each primal decision column must be paid for by the resource prices.

dual constraints come from primal columns\text{dual constraints come from primal columns}
Flagship dualThe concrete dual is recomputed from the flagship primal.dual objective44dual constraints211121

Diagram note

The displayed dual objective and constraints are recomputed from the flagship primal. Pixel positions are rounded for layout; every number shown is exact.

build dual, then certify\text{build dual, then certify}
Flagship dualThe concrete dual is recomputed from the flagship primal.dual objective44dual constraints211121