Linear programming question, need help
up vote
-1
down vote
favorite
I'm a MS student taking this linear programming course and I found this question online while studying for an exam. I can't find a way to solve it. I tried using the Dual, but since but problems are min it didn't help much :/
I'm trying to prove the following,
Let $x$ be a feasible point for LP in standard form
minimize $c^Tx$
subject to $Ax = b, xge 0$.
Let
$Z = {i|x_i = 0}$. Prove that $x$ is an optimal solution if and only if the optimal value of the
following LP is 0:
minimize $c^Ty$
subject to $Ay = 0, y_i ge 0$ for all $i in Z$.
Any advise?
Thanks!
linear-algebra
asked Nov 18 at 12:38
John Doe
62
add a comment |
up vote
-1
down vote
favorite
I'm a MS student taking this linear programming course and I found this question online while studying for an exam. I can't find a way to solve it. I tried using the Dual, but since but problems are min it didn't help much :/
I'm trying to prove the following,
Let $x$ be a feasible point for LP in standard form
minimize $c^Tx$
subject to $Ax = b, xge 0$.
Let
$Z = {i|x_i = 0}$. Prove that $x$ is an optimal solution if and only if the optimal value of the
following LP is 0:
minimize $c^Ty$
subject to $Ay = 0, y_i ge 0$ for all $i in Z$.
Any advise?
Thanks!
linear-algebra
asked Nov 18 at 12:38
John Doe
62
Please share what you have tried and your level, so people here can come up with an appropriate answer. Also, please format your equations using mathjax.
– Viktor Glombik
Nov 18 at 12:58
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I'm a MS student taking this linear programming course and I found this question online while studying for an exam. I can't find a way to solve it. I tried using the Dual, but since but problems are min it didn't help much :/
I'm trying to prove the following,
Let $x$ be a feasible point for LP in standard form
minimize $c^Tx$
subject to $Ax = b, xge 0$.
Let
$Z = {i|x_i = 0}$. Prove that $x$ is an optimal solution if and only if the optimal value of the
following LP is 0:
minimize $c^Ty$
subject to $Ay = 0, y_i ge 0$ for all $i in Z$.
Any advise?
Thanks!
linear-algebra
asked Nov 18 at 12:38
John Doe
62
I'm a MS student taking this linear programming course and I found this question online while studying for an exam. I can't find a way to solve it. I tried using the Dual, but since but problems are min it didn't help much :/
I'm trying to prove the following,
Let $x$ be a feasible point for LP in standard form
minimize $c^Tx$
subject to $Ax = b, xge 0$.
Let
$Z = {i|x_i = 0}$. Prove that $x$ is an optimal solution if and only if the optimal value of the
following LP is 0:
minimize $c^Ty$
subject to $Ay = 0, y_i ge 0$ for all $i in Z$.
Any advise?
Thanks!
linear-algebra
linear-algebra
asked Nov 18 at 12:38
John Doe
62
asked Nov 18 at 12:38
John Doe
62
edited Nov 18 at 13:28
asked Nov 18 at 12:38
John Doe
62
asked Nov 18 at 12:38
John Doe
62
asked Nov 18 at 12:38
John Doe
62
62
Please share what you have tried and your level, so people here can come up with an appropriate answer. Also, please format your equations using mathjax.
– Viktor Glombik
Nov 18 at 12:58
add a comment |
Please share what you have tried and your level, so people here can come up with an appropriate answer. Also, please format your equations using mathjax.
– Viktor Glombik
Nov 18 at 12:58
Please share what you have tried and your level, so people here can come up with an appropriate answer. Also, please format your equations using mathjax.
– Viktor Glombik
Nov 18 at 12:58
Please share what you have tried and your level, so people here can come up with an appropriate answer. Also, please format your equations using mathjax.
– Viktor Glombik
Nov 18 at 12:58
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3003483%2flinear-programming-question-need-help%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Please share what you have tried and your level, so people here can come up with an appropriate answer. Also, please format your equations using mathjax.
– Viktor Glombik
Nov 18 at 12:58