{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

dual simplex

# dual simplex - Math 407A Linear Optimization Lecture 11 The...

This preview shows pages 1–12. Sign up to view the full content.

Math 407A: Linear Optimization Lecture 11: The Dual Simplex Algorithm Math Dept, University of Washington

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

View Full Document
The Dual Simplex Algorithm
P maximize - 4 x 1 - 2 x 2 - x 3 subject to - x 1 - x 2 + 2 x 3 ≤ - 3 - 4 x 1 - 2 x 2 + x 3 ≤ - 4 x 1 + x 2 - 4 x 3 2 0 x 1 , x 2 , x 3

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

View Full Document
P maximize - 4 x 1 - 2 x 2 - x 3 subject to - x 1 - x 2 + 2 x 3 ≤ - 3 - 4 x 1 - 2 x 2 + x 3 ≤ - 4 x 1 + x 2 - 4 x 3 2 0 x 1 , x 2 , x 3 D minimize - 3 y 1 - 4 y 2 + 2 y 3 subject to - y 1 - 4 y 2 + y 3 ≥ - 4 - y 1 - 2 y 2 + y 3 ≥ - 2 2 y 1 + y 2 - 4 y 3 ≥ - 1 0 y 1 , y 2 , y 3
P maximize - 4 x 1 - 2 x 2 - x 3 subject to - x 1 - x 2 + 2 x 3 ≤ - 3 - 4 x 1 - 2 x 2 + x 3 ≤ - 4 x 1 + x 2 - 4 x 3 2 0 x 1 , x 2 , x 3 D minimize - 3 y 1 - 4 y 2 + 2 y 3 subject to - y 1 - 4 y 2 + y 3 ≥ - 4 - y 1 - 2 y 2 + y 3 ≥ - 2 2 y 1 + y 2 - 4 y 3 ≥ - 1 0 y 1 , y 2 , y 3 -1 -1 2 1 0 0 -3 -4 -2 1 0 1 0 -4 1 1 -4 0 0 1 2 -4 -2 -1 0 0 0 0

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

View Full Document
P maximize - 4 x 1 - 2 x 2 - x 3 subject to - x 1 - x 2 + 2 x 3 ≤ - 3 - 4 x 1 - 2 x 2 + x 3 ≤ - 4 x 1 + x 2 - 4 x 3 2 0 x 1 , x 2 , x 3 D minimize - 3 y 1 - 4 y 2 + 2 y 3 subject to - y 1 - 4 y 2 + y 3 ≥ - 4 - y 1 - 2 y 2 + y 3 ≥ - 2 2 y 1 + y 2 - 4 y 3 ≥ - 1 0 y 1 , y 2 , y 3 -1 -1 2 1 0 0 -3 -4 -2 1 0 1 0 -4 1 1 -4 0 0 1 2 -4 -2 -1 0 0 0 0 Not primal feasible. Dual feasible!
The tableau below is said to be dual feasible because the objective row coeﬃcients are all non-positive, but it is not primal feasible . -1 -1 2 1 0 0 -3 -4 -2 1 0 1 0 -4 1 1 -4 0 0 1 2 -4 -2 -1 0 0 0 0

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

View Full Document
The tableau below is said to be dual feasible because the objective row coeﬃcients are all non-positive, but it is not primal feasible . -1 -1 2 1 0 0 -3 -4 -2 1 0 1 0 -4 1 1 -4 0 0 1 2 -4 -2 -1 0 0 0 0 A tableau is optimal if and only if it is both primal feasible and dual feasible.
The tableau below is said to be dual feasible because the objective row coeﬃcients are all non-positive, but it is not primal feasible . -1 -1 2 1 0 0 -3 -4 -2 1 0 1 0 -4 1 1 -4 0 0 1 2 -4 -2 -1 0 0 0 0 A tableau is optimal if and only if it is both primal feasible and dual feasible. Can we design a pivot for this tableau that tries to move it toward primal feasibility while retaining dual feasibility?

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

View Full Document
D minimize - 3 y 1 - 4 y 2 + 2 y 3 subject to - y 1 - 4 y 2 + y 3 ≥ - 4 - y 1 - 2 y 2 + y 3 ≥ - 2 2 y 1 + y 2 - 4 y 3 ≥ - 1 0 y 1 , y 2 , y 3
D minimize - 3 y 1 - 4 y 2 + 2 y 3 subject to - y 1 - 4 y 2 + y 3 ≥ - 4 - y 1 - 2 y 2 + y 3 ≥ - 2 2 y 1 + y 2 - 4 y 3 ≥ - 1 0 y 1 , y 2 , y 3 - 1 - 1 2 1 0 0 - 3 - 4 - 2 1 0 1 0 - 4 1 1 - 4 0 0 1 2 - 4 - 2 - 1 0 0 0 0

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.

{[ snackBarMessage ]}

### Page1 / 46

dual simplex - Math 407A Linear Optimization Lecture 11 The...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online