Simplex & Big-M

Reading the tableau

Each row is a constraint in standard form; the b.v. column gives the basic variable for that row. The objective row is written as $Z - c'x + M a = 0$, so a negative entry identifies a variable that can improve the objective. The pivot cell is outlined.

• Slack variables ($s$) turn ≤ into =.
• Surplus variables ($e$) turn ≥ into =.
• Artificial variables ($a$) give the initial basis when there is no slack; they carry the penalty $M$.

Conventions

The tool uses the common $Z$-row convention. Choose the entering variable from the most negative objective coefficient, then apply the ratio test; ties go to the lowest row. Minimisation is solved as the maximisation of $-C$, and the reported value is converted back.

Big-M uses a pair $a + bM$ with $M \to \infty$ treated as arbitrarily large. Pivot decisions follow the exact coefficients, so the tableau matches a hand calculation.

Export

The $\LaTeX$ tab previews the document and lets you copy or download the .tex source. It usesamsmath and array, so a standard TeX installation compiles it and the preview matches the exported tableaus.