Simplex LP Calculator

Model objective functions and constraints quickly with clarity. Review pivot steps, slacks, and optimal values. Export your results for clean planning reports and sharing.

Calculator

Objective Function

Enter coefficients for Z = c1x1 + c2x2 + ... + cnxn.

Constraints

Constraint 1

Constraint 2

Constraint 3

Example Data Table

Part x1 x2 Relation Right Side
Objective 3 5 Maximize Z
Constraint 1 2 3 12
Constraint 2 1 1 5
Constraint 3 1 0 4

Formula Used

The calculator uses the standard simplex tableau idea:

Maximize or minimize: Z = c1x1 + c2x2 + ... + cnxn

Subject to: a11x1 + a12x2 + ... + a1nxn relation b1

Reduced cost: Cj - Zj = Cj - sum(Cb × column values)

Ratio test: right side value divided by positive entering column value

Less than constraints receive slack variables. Greater than constraints receive surplus and artificial variables. Equal constraints receive artificial variables. The Big M penalty helps remove artificial variables from a feasible final basis.

How To Use This Calculator

  1. Select maximize or minimize.
  2. Choose the number of decision variables and constraints.
  3. Enter objective coefficients for each decision variable.
  4. Enter each constraint coefficient, relation sign, and right side value.
  5. Set precision and an iteration limit.
  6. Press the calculate button to show the result above the form.
  7. Use the CSV or PDF buttons to download a report.

What Is a Simplex LP Calculator?

A simplex LP calculator helps solve linear programming problems. It works with an objective function and several constraints. The goal may be profit, cost, time, labor, or material use. The calculator arranges these values into a tableau. Then it applies pivot steps until no better move remains.

Why Simplex Method Matters

Linear programming is useful when resources are limited. A business may need the best production mix. A planner may need the lowest shipping cost. A student may need quick simplex practice. The simplex method gives a structured way to test corner points without checking every possible point by hand.

What This Tool Handles

This tool accepts maximization and minimization models. You can enter several decision variables. You can also choose less than, greater than, or equal constraints. The calculator uses slack, surplus, and artificial variables when needed. It then displays the final decision values, objective value, constraint activity, and pivot log.

Understanding The Output

The optimal value is the best objective result found by the method. Variable values show the chosen level for each decision variable. Slack means unused capacity in a less than constraint. Surplus means extra amount above a required minimum. Artificial values should be zero in a feasible final answer.

Best Use Cases

Use this calculator for study, planning, and quick checking. It is helpful for small production models. It can also support diet, blending, staffing, allocation, and transport style exercises. For very large models, a dedicated optimization package may be better.

Tips For Accurate Results

Enter coefficients carefully. Keep units consistent across all constraints. Use positive right side values when possible. Review each relation sign before solving. If a result shows infeasible, your constraints may conflict. If it shows unbounded, the objective may improve forever under the current limits.

Learning With Tableaus

The pivot log is useful for learning. It shows which column enters and which row leaves. Each step changes the basis. When all reduced costs meet the stopping rule, the current basic solution is optimal.

Interpreting Limits Carefully

The model assumes nonnegative variables. It also assumes coefficients describe a linear system. Nonlinear terms, changing percentages, and conditional rules should be simplified before entry for clearer simplex results.

FAQs

What does a simplex LP calculator do?

It solves linear programming models by moving through simplex tableaus. It finds the best objective value while respecting all entered constraints.

Can I solve minimization problems?

Yes. The calculator converts minimization into an equivalent simplex form. It then reports the original objective value after solving.

What are slack variables?

Slack variables show unused capacity in less than constraints. A zero slack value means that constraint is binding at the result.

What are artificial variables?

Artificial variables create a starting basis for equal and greater than constraints. A feasible final answer should leave them at zero.

Why can a model be infeasible?

A model is infeasible when its constraints conflict. No decision variable combination can satisfy all limits at the same time.

What does unbounded mean?

Unbounded means the objective can improve without a finite stopping point. Usually, a missing upper or lower limit causes this result.

How many variables can this file handle?

This version accepts up to six variables and eight constraints. You can raise these limits in the input validation if needed.

Can I download the solution?

Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.