Linear Programming Calculator - Simplex Method

Solve linear programming problems using the simplex method. Ideal for operations research, economics, and optimization students.

Maximizes or minimizes linear objective functions subject to linear equality and inequality constraints.

About Linear Programming

Linear programming is a mathematical method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. It is widely used in business and economics.

Using This Calculator

Select whether you want to maximize or minimize your objective function
Specify the number of decision variables in your problem
Enter the coefficients for your objective function
Add constraints with their coefficients and right-hand side values
Click "Solve Problem" to see the optimal solution

Example Problem

Maximize: Z = 3x + 4y

Subject to:

x + 2y ≤ 14
3x - y ≥ 0
x - y ≤ 2
x, y ≥ 0

Solution: x = 6, y = 4, Z = 34

Common Applications

Resource allocation in manufacturing
Diet planning with nutritional constraints
Transportation and logistics optimization
Portfolio optimization in finance

Sensitivity Analysis

Adjust objective coefficients to see how the optimal solution changes:

FAQ

What is the simplex method?

The simplex method is an algorithm that solves linear programming problems by moving from one vertex of the feasible region to an adjacent vertex with a better objective value until the optimal solution is found.

What are the limitations of this calculator?

This implementation handles problems with up to 6 variables and 6 constraints. It uses basic simplex method without advanced techniques for degeneracy or cycling.

What if my problem has no solution?

The calculator will indicate if the problem is infeasible (no solution satisfies all constraints) or unbounded (the objective can improve indefinitely).

Linear Programming Calculator - Simplex Method

Problem Setup

Solution

Simplex Tableau Visualization

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