Leaving Variables

The leaving variable is the basic variable that reaches zero first as the entering variable increases.

Direction Column

After choosing entering $x_j$, compute $u=B^{-1}A_j$.

Basic Values

They change as $x_B(\theta)=x_B-\theta u$.

Eligible Rows

Only rows with $u_i>0$ can limit $\theta$.

Leaving Rule

Choose the smallest ratio $x_{B(i)}/u_i$ among $u_i>0$.

Checklist

Compute $u$, ratios, and the leaving row.

See Also

• Minimum Ratio Test
• Basis Updates

Exam checkpoint

For simplex questions in minimization form, negative reduced costs indicate possible improvement. Use $u=B^{-1}A_j$, apply the ratio test only to positive components of $u$, then update the basis.