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Linear Optimization

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.

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Linear Optimization

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  1. Linear Optimization Lecture 1: Introduction Instructor: TsvetanAsamov

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

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

  4. Example

  5. Diet Problem Formulation

  6. Linear Programming Examples

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

  8. Standard Form

  9. Diet Problem • Objective function • Feasible solution • Optimal solution • Optimal value: 92.5

  10. Linear programming problems • Unique optimal solution • Many optimal solutions • No optimal solutions • Infeasible problems

  11. Linear programming problems • Unique optimal solution • Many optimal solutions • No optimal solutions • Infeasible problems • Unbounded problems

  12. Problems

  13. Problems

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

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