Analyze constraints, intersections, and optimal values clearly. Compare feasible points using inputs and visual aids. Download reports and graphs for smarter optimization work today.
This tool solves two-variable linear programs using the graphical corner-point method.
Objective function: Z = c1x + c2y
Constraints: aix + biy ≤, ≥, or = di
Non-negativity: x ≥ 0 and y ≥ 0
Optimization rule: Evaluate Z at every feasible corner point, then choose the largest value for maximization or the smallest value for minimization.
This page uses the graphical corner-point method for two decision variables. Constraint lines are intersected in pairs, feasible points are filtered, and the objective function is tested at each feasible corner.
| Item | Value |
|---|---|
| Objective | Maximize Z = 5x + 4y |
| Constraint 1 | 6x + 4y ≤ 24 |
| Constraint 2 | x + 2y ≤ 6 |
| Constraint 3 | -x + y ≤ 1 |
| Non-negativity | x ≥ 0, y ≥ 0 |
| Optimal solution | x = 3, y = 1.5, Z = 21 |
It solves two-variable linear programming problems with a linear objective function and linear constraints. It identifies feasible corner points, evaluates the objective value, and shows the best bounded solution when one exists.
Yes. You can choose either mode. The calculator tests the objective value at each feasible corner point and returns the largest value for maximization or the smallest value for minimization.
This page uses a graphical corner-point approach, which is most practical for two decision variables. More variables usually require simplex or other matrix-based optimization methods.
If the constraints conflict and no point satisfies all of them together, the result is marked infeasible. In that case, no feasible region and no valid optimum can be reported.
An unbounded result means the feasible region lets the objective improve forever in the chosen direction. The calculator reports that no finite maximum or minimum is available.
For linear programming with a bounded feasible region, the optimal value occurs at a corner point. That property makes corner-point testing a reliable method for two-variable models.
Yes. After solving, you can download a CSV summary or generate a PDF report containing the status, objective details, feasible points, and optimal solution information.
Use any consistent units that fit your model. For example, x and y may represent labor hours, product quantities, or shipping loads, as long as every coefficient matches the same scale.
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.