Mathematical Methods of Engineering Analysis
2 SETS AND FUNCTIONS Subsets A set A is said to be a subset of a set B if every element of A is an element of B. We write A ⊂ B or B ⊃ A to indicate it and use expressions like A is contained in B,
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ORF 522: Lecture 7 Linear Programming: Chapter 7 ...
vanderbei.princeton.eduORF 522: Lecture 7 Linear Programming: Chapter 7 Sensitivity and Parametric Analysis Robert J. Vanderbei October 3, 2013 Slides last edited at 1:24pm on Thursday 3rd October, 2013 Operations Research and Financial Engineering, Princeton University
Linear Programming: Chapter 7 Sensitivity and Parametric ...
vanderbei.princeton.eduLinear Programming: Chapter 7 Sensitivity and Parametric Analysis Robert J. Vanderbei October 17, 2007 Operations Research and Financial Engineering
Linear Programming: Chapter 5 Duality
vanderbei.princeton.eduResource Allocation Recall the resource allocation problem (m = 2, n = 3): maximize c 1x 1 + c 2x 2 + c 3x 3 subject to a 11x 1 + a 12x 2 + a 13x 3 b 1 a 21x 1 + a 22x 2 + a 23x 3 b 2 x 1; x 2; x 3 0; where c j = pro t per unit of product j produced b i = units of raw material i on hand a ij = units raw material i required to produce 1 unit of prod j:
Linear Programming: Chapter 2 The Simplex Method
vanderbei.princeton.eduSimplex Method|First Iteration If x 2 increases, obj goes up. How much can x 2 increase? Until w 4 decreases to zero. Do it. End result: x 2 >0 whereas w 4 = 0. That is, x 2 must become basic and w 4 must become nonbasic. Algebraically rearrange equations to, in the words of Jean-Luc Picard, "Make it so." This is a pivot.
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