Understanding Linear Programming
Linear programming is a method for choosing the best value under limits. It works when the goal is linear. It also needs linear restrictions. The calculator uses two decision variables, called x and y. This makes the result easy to view by the corner point method.
Why Corner Points Matter
A feasible region is the area that satisfies every constraint. Its borders come from the constraint lines. When a best answer exists, it appears at a corner point. The tool finds line intersections, checks each point, then tests the objective value. This gives clear steps, not only a final number.
Useful Inputs
Start with an objective function, such as maximize profit or minimize cost. Then enter each restriction. A restriction can be less than, greater than, or equal to a limit. Nonnegative settings keep x and y from going below zero. This is common in production, diet, transport, and resource planning problems.
Reading The Result
The result table lists feasible vertices. It shows the objective value at each point. The best row is chosen from that list. If the problem is a maximization task, the largest value is selected. If it is a minimization task, the smallest value is selected. The steps show how boundaries and intersections are used.
Advanced Uses
You can model many classroom and business cases. Products may use labor, machine hours, and material. A diet plan may control calories, protein, and cost. A transport model may balance demand and capacity. The tool is best for two variable problems. It also supports quick comparison of many possible planning choices. These checks reduce common manual mistakes. Larger models usually need simplex or matrix based solvers.
Checking Accuracy
Use consistent units in every row. Do not mix hours with minutes. Check each inequality sign. A reversed sign can change the feasible region. Round only after the final result when possible. The precision box controls display rounding. It does not change the main method.
Exporting Work
Download the CSV file for spreadsheets. Download the PDF report for sharing. Both exports include the main result and tested vertices. This helps show work in assignments or reports. Keep the entered data with your notes. It makes review easier later.