zeeshas901 Posted February 16, 2020 Share Posted February 16, 2020 (edited) Hello! I need urgent help regarding the following question. Any help will be greatly appreciated. Thank you! Edited February 16, 2020 by zeeshas901 question is added as an attachment Link to comment Share on other sites More sharing options...
taeto Posted February 16, 2020 Share Posted February 16, 2020 (edited) I do not see an immediate solution. But is it not just a linear programming (LP) problem? Clearly you want to maximize a linear function of the matrix entries subject to several linear equality and inequality conditions, the nonnegativity, sum of row entries, and the condition \(b_1A=b_2\) which is equivalent to \(n\) linear equations. So unless I am missing something, the solution will just be standard. Edit: I notice that linear programming is already one of the tags for the question posed on a different site. Have you tried to look at the dual linear program (DLP) to the given LP? Edited February 16, 2020 by taeto Link to comment Share on other sites More sharing options...
taeto Posted February 16, 2020 Share Posted February 16, 2020 (edited) I still do not know if this is a homework question. But let us try a small example. If we have \(b_1 = (1/2,1/2)\) and \(b_2 = (2/3,1/3),\) do you know how to determine the matrix \(A?\) Do you see why trace\((A) = 5/3 \) is the optimum and \(A\) is uniquely determined? Edited February 16, 2020 by taeto Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now