Introduction to Linear Programming - Department of Mathematics

184 Pages·2012·0.57 MB·English

Linear Programming
Lecture 2: Introduction to Linear Programming
Lecture 2: Introduction to Linear Programming Linear Programming 1 / 46
1 Math 407: Introduction
2 What is linear programming?
3 Applications of Linear Programing
4 Example: Plastic Cup Factory
5 Introduction to LP Modeling
6 Graphical Solution of 2D LPs
7 Introduction to Sensitivity Analysis
8 The Theory of Linear Economic Models
Production Models
The Optimal Value Function and Marginal Values
Duality: The Hidden Hand of the Market Place
9 LP Duality
The Weak Duality Theorem of Linear Programming
Lecture 2: Introduction to Linear Programming Linear Programming 2 / 46
A mathematical optimization problem is one in which some function is either
maximized or minimized relative to a given set of alternatives.
The function to be minimized or maximized is called the objective function.
The set of alternatives is called the feasible region (or constraint region).
n
In this course, the feasible region is always taken to be a subset of R (real
n
n-dimensional space) and the objective function is a function from R to R.
What is optimization?
Lecture 2: Introduction to Linear Programming Linear Programming 3 / 46
The function to be minimized or maximized is called the objective function.
The set of alternatives is called the feasible region (or constraint region).
n
In this course, the feasible region is always taken to be a subset of R (real
n
n-dimensional space) and the objective function is a function from R to R.
What is optimization?
A mathematical optimization problem is one in which some function is either
maximized or minimized relative to a given set of alternatives.
Lecture 2: Introduction to Linear Programming Linear Programming 3 / 46
The set of alternatives is called the feasible region (or constraint region).
n
In this course, the feasible region is always taken to be a subset of R (real
n
n-dimensional space) and the objective function is a function from R to R.
What is optimization?
A mathematical optimization problem is one in which some function is either
maximized or minimized relative to a given set of alternatives.
The function to be minimized or maximized is called the objective function.
Lecture 2: Introduction to Linear Programming Linear Programming 3 / 46
n
In this course, the feasible region is always taken to be a subset of R (real
n
n-dimensional space) and the objective function is a function from R to R.
What is optimization?
A mathematical optimization problem is one in which some function is either
maximized or minimized relative to a given set of alternatives.
The function to be minimized or maximized is called the objective function.
The set of alternatives is called the feasible region (or constraint region).
Lecture 2: Introduction to Linear Programming Linear Programming 3 / 46
What is optimization?
A mathematical optimization problem is one in which some function is either
maximized or minimized relative to a given set of alternatives.
The function to be minimized or maximized is called the objective function.
The set of alternatives is called the feasible region (or constraint region).
n
In this course, the feasible region is always taken to be a subset of R (real
n
n-dimensional space) and the objective function is a function from R to R.
Lecture 2: Introduction to Linear Programming Linear Programming 3 / 46
A linear program is an optimization problem in finitely many variables
having a linear objective function and a constraint region determined
by a finite number of linear equality and/or inequality constraints.
What is linear programming (LP)?
Lecture 2: Introduction to Linear Programming Linear Programming 4 / 46
What is linear programming (LP)?
A linear program is an optimization problem in finitely many variables
having a linear objective function and a constraint region determined
by a finite number of linear equality and/or inequality constraints.
Lecture 2: Introduction to Linear Programming Linear Programming 4 / 46
A linear program is an optimization problem
in finitely many variables
having a linear objective function
and a constraint region determined by a
finite number of constraints
that are linear equality and/or linear inequality constraints.
What is linear programming (LP)?
Lecture 2: Introduction to Linear Programming Linear Programming 5 / 46