Calculator
Example Data Table
| Model part | x1 | x2 | Relation | Right side |
|---|---|---|---|---|
| Maximize profit | 40 | 30 | ||
| Material limit | 2 | 1 | ≤ | 100 |
| Labor limit | 1 | 1 | ≤ | 80 |
| Machine limit | 1 | 0 | ≤ | 40 |
Formula Used
Objective function: Z = c1x1 + c2x2 + c3x3
Constraints: a1x1 + a2x2 + a3x3 ≤, ≥, or = b
Nonnegative rule: x1 ≥ 0, x2 ≥ 0, x3 ≥ 0
Corner point method: active constraints are solved as equalities. Each point is tested for feasibility. The best feasible objective value is selected.
How to Use This Calculator
- Select maximize or minimize.
- Choose two or three decision variables.
- Enter the objective coefficients.
- Enter each constraint coefficient, sign, and right side value.
- Leave unused constraint rows blank.
- Press Submit to view the result above the form.
- Download the CSV or PDF report when needed.
Linear Programming Calculator Guide
Linear programming is a method for choosing the best result under fixed limits. It is used in production, shipping, finance, diet planning, staffing, and many classroom problems. This calculator turns a model into a clear numerical search. It accepts two or three decision variables, an objective function, and several constraints. Then it checks feasible corner points and selects the strongest value.
Why corner points matter
A linear programming model has straight boundary lines or planes. The best solution usually appears at a corner of the feasible region when a bounded optimum exists. That idea makes the calculator practical. It forms possible active constraint sets. It solves them as equalities. It then tests each point against every original restriction.
Practical model building
Start by defining what each variable represents. Use positive values for resources, units, hours, or product amounts. Write the objective as a maximum profit, minimum cost, or another measurable target. Next, enter each limit with matching coefficients. Choose less than, greater than, or equal signs carefully. A wrong sign can change the entire answer.
Interpreting the answer
The result panel shows the optimal value, the variable values, feasibility notes, and evaluated constraints. Review the binding rows first. A binding constraint is tight at the solution. It often explains the limiting resource. Nonbinding rows show unused capacity or extra space. These details help you explain the answer instead of copying a number.
Advanced use cases
The calculator can compare maximization and minimization cases. It can include equality restrictions and nonnegative variable rules. It is useful for checking hand work, testing textbook examples, and preparing reports. For larger industrial models, dedicated optimization software may still be needed. This tool is best for small transparent models where every step should remain visible.
Exporting your work
Use the CSV export for spreadsheets. Use the PDF export for a clean printable summary. Keep the example table nearby when learning the input pattern. A good model begins with clear variables and units. Once those are correct, the calculation becomes easier to trust and share with teammates later.
FAQs
1. What is a linear programming problem?
It is an optimization problem with a linear objective and linear constraints. The goal is usually to maximize profit, minimize cost, or choose the best mix of resources.
2. How many variables can this calculator solve?
This page supports two or three decision variables. That keeps the corner point method clear and easy to review for study, planning, and reports.
3. Can I enter greater than constraints?
Yes. Choose the greater than or equal relation in the constraint row. The calculator converts it internally and checks feasibility after solving possible corner points.
4. What does binding mean?
A binding constraint is exactly tight at the solution. Its slack is zero or nearly zero. It often shows which resource limits the best outcome.
5. What does infeasible mean?
Infeasible means no point satisfies all entered constraints together. Check signs, right side values, and coefficients. One incorrect row can make the model impossible.
6. What does unbounded mean?
Unbounded means the objective can keep improving without a finite best value. This usually happens when important limiting constraints are missing.
7. Why are nonnegative variables assumed?
Most linear programming models represent quantities, hours, units, or resources. These values usually cannot be negative, so the calculator applies standard nonnegative rules.
8. Can I export the solution?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple printable report that includes the main result and constraint checks.