IOE510+Lecture+03+08+10+Mon

# IOE510+Lecture+03+08+10+Mon - IOE 510 Linear Programming I...

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1 IOE 510 Linear Programming I Monday March 8, 2010 Professor Amy Cohn

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2 Announcements Problem set 8 due Wednesday Last day for exam re-grades
3 Re-cap from Last Time Finalizing simplex method “Big-M” method for generating initial BFS Some observations about degeneracy

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4 Today Something (almost) completely new: duality Parking example
5 Duality

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6 Motivation How can we implicitly enforce a constraint? For every linear program (called the primal problem ) there exists a corresponding dual problem with the same optimal objective value Dual problems are useful for: Sensitivity analysis An alternative solution method Theoretical underpinnings for developing algorithms
7 An Example P: Min 2x + 3y + 4z St 3x + 2y + z > 9 x, y, z > 0 An optimal solution: An optimal solution: (3, 0, 0) with objective value 6 (3, 0, 0) with objective value 6 z z *

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8 An Example P: Min 2x + 3y + 4z St 3x + 2y + z > 9 x, y, z > 0 What about solution (8/3, 0, 0)? What about solution (8/3, 0, 0)?
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## This note was uploaded on 04/11/2010 for the course IOE 510 taught by Professor Staff during the Fall '08 term at University of Michigan.

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IOE510+Lecture+03+08+10+Mon - IOE 510 Linear Programming I...

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