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I have a linear program:

$\min. L(b_{ij})=\sum_i\sum_j w_{ij} b_{ij}$

subject to

$\ 2 \leq \sum_j b_{ij} \leq 3 \ \ \ \forall i$

$ \sum_i b_{ij} = 1 \ \ \ \forall j$

$0\leq b_{ij}\leq1$

$i\in\{1,2\},\ \ j\in\{1,2,3,4,5\}$

My variables are $b_{ij}$ and all of $w_{ij}$ are known constants. I want a closed form for $b_{ij}$. I'm not sure, but probably the Lagrangian method do the job. I'm a computer engineer and not familiar with such mathematics.


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Georg Dantzig's Simplex Method is a way to solve any LP. But I doubt if there is a closed form solution. Else the need of the algorithm would be obsolete as we could just plug in the values. –  Gautam Shenoy Nov 28 '12 at 17:53
If I could use Lagrangian method regarding the first constraint? I have seen Lagrangian method only for $=$ and $\leq$ but not both $\leq$ and $\geq$. –  remo Nov 28 '12 at 18:31
Multiply both sides by minus sign. Inequality flips:) Now use it. –  Gautam Shenoy Nov 28 '12 at 18:40
but joriki says I must include only one of the constraints for each i, and I can not include both, because they are not compatible. –  remo Nov 28 '12 at 18:56

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