1. Linear Optimization Lecture 1: Introduction Instructor: Tsvetan Asamov

2. Elementary Linear Programming with Applications, 2 nd 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

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