ornotes3-2007 - Matrix Notation Max CX s.t. (X is a vector...

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

View Full Document Right Arrow Icon
Matrix Notation Max CX (X is a vector with n elements) s.t. AX b (there are m constraints) and X 0 Convert by adding slacks so that S = b – AX So the constraints are now AX + IS = b where I is an identity matrix of dimension m x m Redefine the X vector to contain both the original X's and the slacks. Redefine the C vector to contain the original C along with the zeros for the slacks, and the new A matrix will contain the original A matrix along with the identity matrix for the slacks. Max CX (X is a vector with n + m elements) s.t. AX b (A has dimensions m, n+m) The A matrix is not square, so it can't be inverted. Basic and nonbasic variables z The solution to the LP problem will have a set of potentially nonzero variables equal in number to the number of constraints. z Such a solution is called a Basic Solution and the associated variables are commonly called Basic Variables . z The other variables are set to zero and are called the nonbasic variables . z Note: if there are 3 constraints, no more than 3 X variables can be non-zero and so on.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Partition the problem MAX C B X B B B + C NB X NB s.t. A B X B B B + A NB X NB = b X B , X B NB 0. Subscript B represents basic variables and NB, non-basic (0 valued) variables and corresponding coefficients. AB will be square because only as many variables as there are constraints can be in the solution. Your text calls this matrix "B" for basis matrix.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/15/2011 for the course AGEC 7100 taught by Professor Duffy,p during the Fall '08 term at Auburn University.

Page1 / 5

ornotes3-2007 - Matrix Notation Max CX s.t. (X is a vector...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online