After a variable enters, the ratio test decides which basic variable must leave. This lesson computes the allowable step lengths exactly. The smallest positive ratio is the one that preserves feasibility.
highlighted = computed this step
Positive ratios
For the x column, the ratios are 2 and 4. Why: the ratio test asks how far x can increase before a slack reaches zero.
ratios 2,4
Leaving row
The smaller ratio is 2, so the first slack leaves. Why: choosing the larger ratio would step past a constraint and lose feasibility.
min=2
Diagram note
The pivot element is the intersection of the recomputed entering column and leaving row. Pixel positions are rounded for layout; every number shown is exact.