dalsegno

dalsegno · 2D Graphical method for linear programming

The graphical method allows solving linear programming problems with two variables: each constraint defines a half-plane, the intersection of all of them is the feasible region (a polygon). The optimum is reached at one of the vertices of the polygon; the objective function is evaluated at each vertex and the maximum or minimum is taken according to the problem's sense.

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