Linear Programming: Formulation and Graphical Solution
Linear programming maximizes or minimizes a linear objective subject to linear constraints. Decision variables represent quantities to be chosen.
Summary
Linear programming maximizes or minimizes a linear objective subject to linear constraints. Decision variables represent quantities to be chosen. An objective such as assigns fixed per-unit contributions, while a resource constraint such as limits resource use. Nonnegativity restrictions exclude negative quantities when these are inappropriate.
For two variables, plot constraint boundaries and identify the intersection of all permitted half-planes. This intersection is the feasible region. Find its vertices, including relevant intersections with coordinate axes, and compare their objective values. For a feasible model with nonnegative variables and a finite optimum, at least one vertex is optimal.
🧠 Key Concepts
- Decision Variables
- Objective Function
- Feasible Region
- Nonnegativity Restrictions
- Corner Point Principle
- Binding Constraints
- Multiple Optima
- Unbounded Objective
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Linear Programming: Formulation and Graphical Solution
📘 Overview Linear programming maximizes or minimizes a linear objective subject to linear constraints. For two decision variables, the graphical method identifies the feasible region and compares objective values at its vertices. A model may have a unique optimum, multiple optima, no feasible solution, or an unbounded objective.
🧠 Key Idea Constraints determine which solutions are permitted; the objective function determines which permitted solution is best. For a feasible two-variable model with nonnegative variables and a finite optimum, at least one vertex is optimal.
⚔️ Core Details: - Decision variables represent unknown quantities to be chosen, such as quantities of two products denoted by and . - The objective has the form
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