Exercise 3.4. Consider the equality-constrained linear program: minimize c"x subject toAx = b. If this problem has a bounded minimum l*, show the following:(i) l* = c"ã = c"î for any two feasible points and î;(ii) l* = b"X = b"î for any two sets of Lagrange multipliers Ā and A.

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Answered: Exercise 3.4. Consider the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following LP model and it is graphical solution to answer questions from a) to g). Maximize z= 4x,+5x2 Subject to: X:5 .(1) 2x:+X;512 ..(2) X,+2x;s12 ..(3) X1, X220.. .(4) 12 11 10 D A *9 10 11 12 n a) What is the optimal solution x1, X2 and z? b) Determine the optimality range of the objective function coefficient c1. c) Determine the feasibility range of the right-hand side for constraint 1, 2 and 3. d) How many basic feasible solutions in this problem? e) Is there any binding constraint(s)? f) Dose any constraint has a slack? which one and by how much? g) Dose any constraint has a surplus? which one and by how much?
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Exercise 3.4. Consider the equality-constrained linear program: minimize cʻx subject to Ax = b. If this problem has a bounded minimum l“, show the following: (i) l* = c"ï = c"î for any two feasible points i and î; (ii) l* = b" Ã = bTî for any two sets of Lagrange multipliers Ā and Â.