Explore constraint systems through clean inputs and clear graphs. See vertices and optimization summaries instantly. Build confidence with structured outputs for every linear model.
| Constraint | Expression | Meaning |
|---|---|---|
| C1 | x + y ≤ 8 | Total combined usage cannot exceed 8 units. |
| C2 | x + 2y ≤ 10 | Weighted capacity places a tighter cap on y. |
| C3 | x ≥ 0 | Negative x values are not allowed. |
| C4 | y ≥ 0 | Negative y values are not allowed. |
| Objective | Max Z = 3x + 2y | Compares every feasible corner for the best value. |
For this example, the corner points are (0,0), (8,0), (6,2), and (0,5). The best value is 24 at (8,0).
ax + by ≤ c, ax + by ≥ c, or ax + by = c
a₁x + b₁y = c₁ and a₂x + b₂y = c₂
x = (c₁b₂ − b₁c₂) / (a₁b₂ − a₂b₁)
y = (a₁c₂ − c₁a₂) / (a₁b₂ − a₂b₁)
Z = p x + q y
The calculator evaluates Z at each feasible corner point. For bounded regions, the best linear-programming solution occurs at a corner.
Area = ½ |Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|
It is the shared set of all points that satisfy every entered inequality and equality at the same time. Any valid solution must lie inside this region or on its boundary.
For linear objective functions over bounded feasible regions, the best value occurs at a corner point. Checking vertices makes optimization faster and easier to verify.
Yes. Use the equals sign when a boundary must be met exactly. Equalities can reduce the feasible region to a line segment or even a single point.
The result will show no feasible solution. This means no point in the plane can satisfy all entered conditions simultaneously.
An objective is unbounded when the feasible region extends infinitely in a direction that keeps improving the selected maximize or minimize target.
No. Area is shown only when the feasible region is bounded and forms a closed polygon. Unbounded regions do not have a finite enclosed area.
Enable it when x and y cannot be negative in your problem. Many production, budget, and resource models require that assumption.
It plots the constraint boundaries and a clipped preview of the feasible region. The preview helps you visually confirm whether the entered system behaves as expected.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.