What This Calculator Solves
A linear program searches for the best value of a linear objective. It uses straight line constraints. This calculator handles two decision variables, named x and y. You can maximize profit, minimize cost, or test a planning model. The tool checks every feasible corner point. That method works because an optimal finite answer occurs at a vertex for this type of model.
Why Vertex Testing Matters
Each constraint draws a boundary line. The allowed side forms the feasible region. When several limits overlap, they create corners. The calculator intersects boundary pairs, filters infeasible points, and evaluates the objective at each remaining point. It also checks axes when nonnegative variables are required. This helps you see why the selected point is optimal.
Planning Uses
Students can test homework models quickly. Analysts can compare production mixes, labor limits, diet targets, shipping plans, and budget allocations. The calculator is also helpful for teaching. It lists candidate points, objective values, slack, surplus, and binding constraints. These details make the result easier to audit.
Understanding Slack
Slack shows unused capacity for a less than or equal constraint. Surplus shows how far a greater than or equal target is exceeded. A binding constraint has almost no slack or surplus. Binding limits often explain the final plan. They are the boundaries that shape the chosen corner.
Good Input Practice
Use consistent units before solving. Keep coefficients in the same scale. For example, do not mix minutes and hours in one labor constraint. Enter negative coefficients only when the model truly needs them. Review every inequality sign carefully. A reversed sign can change the answer completely.
Result Limits
This calculator is designed for two variables. Larger linear programs need matrix methods such as simplex or interior point algorithms. Still, two variable models are powerful. They show the geometry behind optimization. They also help users learn how constraints, objective direction, and feasibility connect.
Final Advice
Start with a simple example. Confirm the feasible region. Then add real numbers. Download the CSV or PDF report after solving. The exported report helps document assumptions, formulas, and final values for review.
Save the scenario name, because it keeps reports easy to trace during later model revisions and audits.