Outline SILICON CHIP CORPORATION Range Analysis for Objective Coecients Resource Variations, Marginal Values, and Ran
Math 407A: Linear Optimization
Lecture 20
Math Dept, University of Washington
March 5, 2010
Lecture 20: Math 407A: Linear Optimization
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Outline SILICON CHIP CORPORATION Pricing Out The Fundamental Theorem on Sensitivity Analysis Concrete Products Corp
Math 407A: Linear Optimization
Lecture 22
Math Dept, University of Washington
November 30, 2009
Lecture 22: Math 407A: Linear Optimization
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MATH 407
MIDTERM EXAM EXAM OUTLINE
November 6, 2009 SAMPLE
Calculators are not allowed for this exam. The exam will consist of 6 questions. Questions 1-4 are worth 50 points each and questions 5 and 6 are worth 25 points each for a total of 250 points. Th
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MATH 407 QUIZ
NAME (Please print): Solutions
There are 2 problems. Stop now and make sure you have both problems. If you do not have them both, then request a new quiz. The rst problem is worth 30 points and the second is worth 45 points for a total of 75
MATH 407 QUIZ
NAME (Please print): Solutions
There are 2 problems. Stop now and make sure you have both problems. If you do not have them both, then request a new quiz. The rst problem is worth 30 points and the second is worth 45 points for a total of 75
3
Does the Simplex Algorithm Work?
In this section we carefully examine the simplex algorithm introduced in the previous chapter. Our goal is to either prove that it works, or to determine those circumstances under which it may fail. If the simplex does n
4
(P )
Duality Theory
maximize subject to cT x Ax b, 0 x
Recall from Section 1 that the dual to an LP in standard form
is the LP (D ) minimize subject to bT y AT y c, 0 y.
Since the problem D is a linear program, it too has a dual. The duality terminology
5
LP Geometry
We now briey turn to a discussion of LP geometry extending the geometric ideas developed in Section 1 for 2 dimensional LPs to n dimensions. In this regard, the key geometric idea is the notion of a hyperplane. Denition 5.1 A hyperplane in R
6
Sensitivity Analysis
In this section we study general questions involving the sensitivity of the solution to an LP under changes to its input data. As it turns out LP solutions can be extremely sensitive to such changes and this has very important pract