dalsegnodalsegno · PL

State the problem

Enter the objective function and constraints. With 2 variables the feasible region and optimum will be shown; with more variables Simplex will be used and, if applicable, the projection onto x₁, x₂.

Problem editor

Use "Apply changes" to create a snapshot (undo/redo).

Press Enter or click outside to update.

Bounds per variable

Form a ≤ xᵢ ≤ b. Leave empty = no bound (∞ or −∞). Default: 0 ≤ xᵢ.

≤x1≤
≤x2≤

Objective function

z =
x1 +
x2

Constraints

x1 +
x2
x1 +
x2
x1 +
x2
View:

Result

Status: Optimal
Optimal value
z* = 10.000000
Solution
x* = (2.000000, 2.000000)
x1* = 2.000000; x2* = 2.000000

Feasible region and optimum

What is linear programming?

Linear programming (LP) is an optimization technique for problems with a linear objective function and linear constraints. It is used in logistics, production, finance and many engineering fields.

This calculator solves linear programming problems in an educational way: with the graphical method for 2 variables (feasible region, vertices, optimum) and with the Simplex algorithm step by step for any number of variables, showing the tableau, pivoting and each elementary operation.

dalsegno · Linear Programming Calculator

Educational tool to solve linear optimization problems with the Simplex method (step by step) and the graphical method in 2D.