The optimal tableau contains more than the primal solution. This lesson reads the decision values, the objective value, and the shadow prices from the final rows. The dual-value check previews why these prices matter.
highlighted = computed this step
Read the optimum
The optimal tableau reads x,y as (4/3, 4/3) and z=8/3. Why: basic decision columns carry their values in the right side.
z=8/3
Shadow prices
The slack-column entries in the z-row are 1/3 and 1/3. Why: these are the shadow prices attached to the two resources.
shadow prices 1/3,1/3
Dual value
The dual value is 4 times 1/3 plus 4 times 1/3=8/3. Each product is 4/3. Why: equality of these values is the strong-duality payoff previewed by the tableau.
dual value =8/3
Diagram note
The optimum and shadow prices are read from the final tableau, then checked by exact multiplication. Pixel positions are rounded for layout; every number shown is exact.