L03f05

# L03f05 - Chapter 1 An Introduction 1 Chek Beng Chua Recap...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 1: An Introduction 1 Chek Beng Chua Recap Terminology • Objective function • Constraints • Feasible solution • Feasible region • Objective value • Optimal solution • Optimal value Geometry of LP (Orange Factory Problem)- x 1 6 x 2 A A A A A A @ @ @ @ @ @ @ @ b (0,0) b (0,4) b (1,5) b (4,2) b (5,0) Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 2 x 1 + 3 x 2 = 17 More Examples: A transportation problem minimize p i =1 q j =1 c ij x ij subject to q j =1 x ij = s i ( i = 1 , 2 , . . . , p ) p i =1 x ij = t i ( j = 1 , 2 , . . . , q ) x ij ≥ i = 1 , 2 , . . . , p, j = 1 , 2 , . . . , q Chapter 1: An Introduction 2 Chek Beng Chua Some More Examples Overdetermined System of Equations n j =1 a ij x j = b i ( i = 1 , 2 , . . . , m ) Suppose the system does not have a solution. Problem: Find x ∈ R n that is “closest” to solving the system. Error of solution x is m i =1 e i where e i := n j =1 a ij x j- b i Mathematical model minimize m i =1 n j =1 a ij x j- b i Not an LP! Convert to LP minimize m i =1 e i subject to n j =1 a ij x j- b i = e i ( i = 1 , 2 , . . . , m ) Chapter 1: An Introduction 3 Chek Beng Chua...
View Full Document

## This note was uploaded on 06/11/2011 for the course C 350 taught by Professor Wolkowicz during the Fall '97 term at Waterloo.

### Page1 / 11

L03f05 - Chapter 1 An Introduction 1 Chek Beng Chua Recap...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online