Maximize or minimize a linear objective function z = ax + by subject to linear constraints.
Objective Fxn
Objective
Max z =
x +
y
Constraints
x ≥ 0, y ≥ 0
x + y ≤
2x + y ≤
Optimization Result
Optimal Value (z*)9.00
At Point (x*, y*)(1.00, 3.00)
This simplified tool optimizes over a region defined by specific standard constraints. Real-world LP solvers handle arbitrary matrices of constraints.
About this calculator
Linear Programming
Linear Programming (LP) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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Pro Tips
Vertex Theorem: The optimal solution always lies at a vertex (corner point) of the feasible region.
Feasible Region: The set of all possible points that satisfy the constraints.
Unbounded: Usually LP problems have constraints that bound the region.
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Fun Facts
"Developed by Kantorovich and Dantzig in the 1940s for military logistics."
"Used extensively in supply chain management, energy planning, and finance."
"The Simplex algorithm is one of the top 10 algorithms of the 20th century."
