Why in every Linear Programming problem in standard form it's assumed that $m\leq n$ (where m are the rows and n the columns of the A matrix) ? Thanks
Asked
Active
Viewed 428 times
0
-
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 – Deepesh Meena Aug 01 '18 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 $m\leq n$ If they are independent and $m>n$ no solution exists. – callculus42 Aug 01 '18 at 14:55
-
@James You probably mean $m<n$. – callculus42 Aug 01 '18 at 15:58
2 Answers
1
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 $m \le n$.
Siong Thye Goh
- 149,520
- 20
- 88
- 149
0
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.
GarryB
- 1