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Number of equations and variables in a Linear Programming problem
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Why in every Linear Programming problem in standard form it's assumed that $mleq n$ (where m are the rows and n the columns of the A matrix) ?
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linear-programming
asked Aug 1 at 14:20
Koinos
485
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Why in every Linear Programming problem in standard form it's assumed that $mleq n$ (where m are the rows and n the columns of the A matrix) ?
Thanks
linear-programming
asked Aug 1 at 14:20
Koinos
485
if m> n then how will you solve for the extra (m-n) variables then you can only obtain the solution in form of the left variables
– James
Aug 1 at 14:32
The missing information in your question is that the "m" equations have to be independent . If this is the case the necceassry condition that the equation system has a solution is $mleq n$ If they are independent and $m>n$ no solution exists.
– callculus
Aug 1 at 14:55
@James You probably mean $m<n$.
– callculus
Aug 1 at 15:58
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Why in every Linear Programming problem in standard form it's assumed that $mleq n$ (where m are the rows and n the columns of the A matrix) ?
Thanks
linear-programming
asked Aug 1 at 14:20
Koinos
485
Why in every Linear Programming problem in standard form it's assumed that $mleq n$ (where m are the rows and n the columns of the A matrix) ?
Thanks
linear-programming
asked Aug 1 at 14:20
Koinos
485
asked Aug 1 at 14:20
Koinos
485
asked Aug 1 at 14:20
Koinos
485
asked Aug 1 at 14:20
Koinos
485
485
if m> n then how will you solve for the extra (m-n) variables then you can only obtain the solution in form of the left variables
– James
Aug 1 at 14:32
The missing information in your question is that the "m" equations have to be independent . If this is the case the necceassry condition that the equation system has a solution is $mleq n$ If they are independent and $m>n$ no solution exists.
– callculus
Aug 1 at 14:55
@James You probably mean $m<n$.
– callculus
Aug 1 at 15:58
add a comment |Â
if m> n then how will you solve for the extra (m-n) variables then you can only obtain the solution in form of the left variables
– James
Aug 1 at 14:32
The missing information in your question is that the "m" equations have to be independent . If this is the case the necceassry condition that the equation system has a solution is $mleq n$ If they are independent and $m>n$ no solution exists.
– callculus
Aug 1 at 14:55
@James You probably mean $m<n$.
– callculus
Aug 1 at 15:58
if m> n then how will you solve for the extra (m-n) variables then you can only obtain the solution in form of the left variables
– James
Aug 1 at 14:32
if m> n then how will you solve for the extra (m-n) variables then you can only obtain the solution in form of the left variables
– James
Aug 1 at 14:32
The missing information in your question is that the "m" equations have to be independent . If this is the case the necceassry condition that the equation system has a solution is $mleq n$ If they are independent and $m>n$ no solution exists.
– callculus
Aug 1 at 14:55
The missing information in your question is that the "m" equations have to be independent . If this is the case the necceassry condition that the equation system has a solution is $mleq n$ If they are independent and $m>n$ no solution exists.
– callculus
Aug 1 at 14:55
@James You probably mean $m<n$.
– callculus
Aug 1 at 15:58
@James You probably mean $m<n$.
– callculus
Aug 1 at 15:58
add a comment |Â
2 Answers
2
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1
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If $m>n$, it means there are redundancy in the constraints of which you can reduce the number of linear equations, hence it suffices to only focus on the case where $m le n$.
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
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Each equality constraint may be used to eliminate one variable, so the standard problem consists only of inequality constraints. Each has a slack or surplus variable added to convert it to an equality, so the number of variables n always exceeds the number of constraints m.
answered Aug 2 at 21:00
GarryB
1
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If $m>n$, it means there are redundancy in the constraints of which you can reduce the number of linear equations, hence it suffices to only focus on the case where $m le n$.
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
add a comment |Â
up vote
1
down vote
If $m>n$, it means there are redundancy in the constraints of which you can reduce the number of linear equations, hence it suffices to only focus on the case where $m le n$.
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If $m>n$, it means there are redundancy in the constraints of which you can reduce the number of linear equations, hence it suffices to only focus on the case where $m le n$.
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
If $m>n$, it means there are redundancy in the constraints of which you can reduce the number of linear equations, hence it suffices to only focus on the case where $m le n$.
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
answered Aug 1 at 14:30
Siong Thye Goh
76.7k134794
76.7k134794
add a comment |Â
add a comment |Â
up vote
0
down vote
Each equality constraint may be used to eliminate one variable, so the standard problem consists only of inequality constraints. Each has a slack or surplus variable added to convert it to an equality, so the number of variables n always exceeds the number of constraints m.
answered Aug 2 at 21:00
GarryB
1
add a comment |Â
up vote
0
down vote
Each equality constraint may be used to eliminate one variable, so the standard problem consists only of inequality constraints. Each has a slack or surplus variable added to convert it to an equality, so the number of variables n always exceeds the number of constraints m.
answered Aug 2 at 21:00
GarryB
1
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Each equality constraint may be used to eliminate one variable, so the standard problem consists only of inequality constraints. Each has a slack or surplus variable added to convert it to an equality, so the number of variables n always exceeds the number of constraints m.
answered Aug 2 at 21:00
GarryB
1
Each equality constraint may be used to eliminate one variable, so the standard problem consists only of inequality constraints. Each has a slack or surplus variable added to convert it to an equality, so the number of variables n always exceeds the number of constraints m.
answered Aug 2 at 21:00
GarryB
1
answered Aug 2 at 21:00
GarryB
1
answered Aug 2 at 21:00
GarryB
1
answered Aug 2 at 21:00
GarryB
1
1
add a comment |Â
add a comment |Â
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if m> n then how will you solve for the extra (m-n) variables then you can only obtain the solution in form of the left variables
– James
Aug 1 at 14:32
The missing information in your question is that the "m" equations have to be independent . If this is the case the necceassry condition that the equation system has a solution is $mleq n$ If they are independent and $m>n$ no solution exists.
– callculus
Aug 1 at 14:55
@James You probably mean $m<n$.
– callculus
Aug 1 at 15:58