Linear Optimization Lecture 1: Introduction Instructor: Tsvetan Asamov.

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Presentation transcript:

Linear Optimization Lecture 1: Introduction Instructor: Tsvetan Asamov

Elementary Linear Programming with Applications, 2 nd edition by Bernard Kolman and Robert E. Beck

Example Need: Energy (2000 kcal), Protein (55 g), Calcium (800 mg)

Example

Diet Problem Formulation

Linear Programming Examples

Linear Programming Objective function Linear equations (equalities) Linear inequalities Linear equations and linear inequalities are referred to as linear constraints

Standard Form

Diet Problem Objective function Feasible solution Optimal solution Optimal value: 92.5

Linear programming problems Unique optimal solution Many optimal solutions No optimal solutions – Infeasible problems

Linear programming problems Unique optimal solution Many optimal solutions No optimal solutions – Infeasible problems – Unbounded problems

Problems

Reading Assignment Review linear algebra – Vectors – Matrices – Matrix multiplication – Matrix inversion – Gauss-Jordan reduction – Linear independence and basis – Subspaces