Convert LP to Canonical Form Calculator

Calculator Form

Example Data Table

Formula Used

The calculator converts each linear programming row into an equality row.

Less Than Or Equal Constraint

a1x1 + a2x2 <= b becomes a1x1 + a2x2 + s = b.

Greater Than Or Equal Constraint

a1x1 + a2x2 >= b becomes a1x1 + a2x2 - e + a = b.

Equality Constraint

a1x1 + a2x2 = b can stay equal. An artificial variable may be added for a starting basis.

Negative Right Side Rule

If b is negative, the full row is multiplied by -1. The inequality direction is flipped.

Objective Row

For maximization, z = c1x1 + c2x2 becomes z - c1x1 - c2x2 = 0.

Variable Sign Rules

A free variable x becomes xp - xn. A nonpositive variable x becomes -y. New variables are nonnegative.

How To Use This Calculator

1. Select whether the original objective is maximize or minimize.
2. Enter objective coefficients in order, separated by commas.
3. Enter variable signs with N, F, or P.
4. Enter each constraint on a separate line.
5. Use the pattern coefficients, relation, and right side.
6. Choose whether artificial variables should be added.
7. Press Calculate to view canonical equations.
8. Use CSV or PDF buttons to save the result.

Convert LP Models With Confidence

Linear programming models often start in mixed wording. A constraint may use less than, greater than, or equality signs. A solver, however, needs a clean structure before simplex work begins. This calculator turns each entered model into a canonical equality system. It keeps the objective visible. It also shows every extra slack, surplus, or artificial variable.

Why Canonical Form Matters

Canonical form makes the model easier to inspect. Each constraint becomes an equation. Nonnegative right hand sides are preferred. Slack variables measure unused capacity. Surplus variables measure excess above a required limit. Artificial variables help create a starting basis when no natural slack basis exists. These details reduce mistakes during tableau setup.

Advanced Input Control

The tool accepts objective coefficients, variable sign choices, and multiple constraints. You can enter less than or equal, greater than or equal, or equal relations. Negative right hand sides are corrected by multiplying the whole row by negative one. The relation is flipped when needed. Free variables can be split into positive and negative parts. Nonpositive variables can be replaced with negative nonnegative variables.

What The Result Shows

The result area appears below the header and above the form. It lists the transformed objective row. It also lists the canonical constraints in equation form. Added variables are named by row, so the output stays readable. A short decision note explains which transformation was applied. The result table can be exported for records. Save both exports after each major revision. This creates a clear traceable record for team checks, audits, tutoring, or future model improvements.

Practical Use Cases

Students can test homework setups before solving them by hand. Teachers can prepare examples for simplex lessons. Analysts can document how raw planning restrictions become solver ready equations. The exported files help keep calculations with project notes. The example table gives ready input patterns for quick testing.

Best Practices

Enter coefficients in the same order everywhere. Keep the objective coefficient count equal to the variable count. Use commas for clarity. Review negative right hand sides before trusting the final row. Confirm whether artificial variables are wanted for your course or solver method. Then copy the canonical equations into your tableau or optimization software.

FAQs