Linear Programming Calculator
Objective Function
Constraints
Non-negativity constraints (x ≥ 0, y ≥ 0) are automatically included
Understanding Linear Programming
Linear Programming (LP) is a mathematical technique for optimizing a linear objective function subject to linear equality and inequality constraints.
Components
- Decision Variables: What we're solving for (x, y)
- Objective Function: What we optimize (Z)
- Constraints: Limitations on resources
- Feasible Region: Area satisfying all constraints
Graphical Method
- Graph all constraints
- Identify the feasible region
- Find corner points (vertices)
- Evaluate objective at each vertex
- Select optimal vertex
Corner Point Theorem
If a linear program has an optimal solution, then at least one optimal solution occurs at a corner point (vertex) of the feasible region. This is why we only need to evaluate the objective function at the vertices.
Common Applications
Production Planning
Maximize profit given limited resources and production capacity
Diet Problems
Minimize cost while meeting nutritional requirements
Transportation
Minimize shipping costs while meeting demand
About Linear Programming Calculator - Graphical Method
Solve two-variable linear programming problems graphically. Visualize constraints, feasible region, and find optimal solutions.
Our **Linear Programming Calculator** solves optimization problems with two variables using the graphical method. Enter your objective function and constraints to visualize the feasible region and find optimal vertex solutions. For larger problems, use our Simplex Method Calculator.
The graphical method plots constraints as lines, identifies the feasible region (intersection of all constraint half-planes), and evaluates the objective function at each vertex. The optimal solution always occurs at a corner point.
Perfect for learning linear programming concepts before moving to algebraic methods. See how constraints interact, understand feasibility and boundedness, and visualize optimization in action.
Key Features
Why Use This Tool?
Common Use Cases
Education: Learn LP fundamentals visually.
Quick Analysis: Two-variable optimization problems.
Verification: Check simplex results graphically.
Demonstrations: Teaching optimization concepts.
Related Tools
How to Use
Enter objective function coefficients
Choose maximize or minimize
Add constraint equations
Select constraint types
Click Solve