Linear Programming Simplex Calculator
Maximize a linear objective for several nonnegative variables with entered upper-bound inequalities.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use a bounded-iteration primal simplex tableau with Bland-style entering/tie rules and verify the final original-constraint residuals.
Maximize c·x subject to Ax≤b and x≥0, starting with the feasible slack basis
Worked example
The default three-variable model has maximum objective 11; x=(3,1,0) is one optimal solution.
Assumptions and input details
Only ≤ inequalities with nonnegative right-hand sides; the origin must be feasible. No equality/≥ constraints, negative variables or integer restrictions. Magnitudes at most 1e6; unbounded/numerically unresolved models are rejected. Multiple optima may exist; this is a numeric planning model, not an operational decision.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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