Lecture4

# Lecture4 - MS&E111 Introduction to Optimization Prof Amin...

This preview shows pages 1–3. Sign up to view the full content.

MS&E111 Lecture 4 Introduction to Optimization April 17, 2006 Prof. Amin Saberi Scribed by: Yusuf Ozuysal 1 Solving a linear program In this lecture, we will talk about the simplex algorithm and how it finds the optimum solution for a linear program. First, we will show how to transform all linear programs to a generic form known as the standard form. 1.1 Standard form A linear program is in standard form if: All its variables are required to be non-negative All of its constraints (except the non-negativity constraints) are in equality form The constants on the right hand side in all constraints are non-negative Every linear program can be written in the standard format. For example, consider the linear program: maximize z = 3 x 1 + 2 x 2 - x 3 + x 4 subject to x 1 + 2 x 2 + x 3 - x 4 5 - 2 x 1 - 4 x 2 + x 3 + x 4 ≤ - 1 x 1 0 , x 2 0 We multiply any constraints in which the right hand side is non-negative by - 1 maximize z = 3 x 1 + 2 x 2 - x 3 + x 4 subject to x 1 + 2 x 2 + x 3 - x 4 5 2 x 1 + 4 x 2 - x 3 - x 4 1 x 1 0 , x 2 0

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

View Full Document
2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern