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