Exercise 5.8. Consider the linear program minimize dTw wER" subject to Gw > f, w > 0, where G is an m × n matrix. (a) Convert this problem to all-inequality form and to standard form. In both cases, use "a" to denote the vector of variables and "A" to denote the matrix of general constraints. (b) Formulate the dual form of the linear program.
Exercise 5.8. Consider the linear program minimize dTw wER" subject to Gw > f, w > 0, where G is an m × n matrix. (a) Convert this problem to all-inequality form and to standard form. In both cases, use "a" to denote the vector of variables and "A" to denote the matrix of general constraints. (b) Formulate the dual form of the linear program.
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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
Transcribed Image Text:Exercise 5.8. Consider the linear program
minimize dTw
wER"
subject to Gw > f, w > 0,
where G is an m × n matrix.
(a) Convert this problem to all-inequality form and to standard form. In both cases,
use "a" to denote the vector of variables and "A" to denote the matrix of general
constraints.
(b) Formulate the dual form of the linear program.
(c) Suppose that you are given a specific problem in the above LP form. Briefly discuss
the circumstances under which you would use the primal or dual form to solve the
problem
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