linear programming - how to write standard form i've created a small linear optimization modell (simplex) in excel. it assigns products to shelfs and minimizes the total distance. My math skills are rusty. how do i write this LP-Modell in the standard form (linear function to be minimized, Problem constraints, Non-negative variables) Thats how it looks like I read several examples, i am confused. In every example there is just one matrice. My model is using 2.. I really tried to understand it. Constraints: for each product one shelf, each self just one product thank you! $\large{\texttt{Edit}}$ When i add more products/shelfes $(n)$ the number of variables grows exponentially $(n^2)$. I think integer programming is not the fasted way to slove this. The hungarian algorithm would be the bedder/faster choice to slove this right? How the matrix would look like

This model is not a real linear problem since the decision variables are binary.

The program is

$\text{min} \ \ z=100x_{11}+50x_{12}+200x_{21}+100x_{22}$

$x_{11}+x_{21}=1$

$x_{12}+x_{22}=1$

$x_{11}+x_{12}=1$

$x_{21}+x_{22}=1$

$x_{ij} \in \\{0,1\\} \ \forall \ \ i,j=1, 2$

This problem can be solved with the solver. I got the solution $x_{11}^*=x_{22}^*=1,x_{12}^*=x_{21}^*=0, z^*=200$