A manufacturing company has a set $I = \left \{ 1,2, ..., i, ..., M \right \}$ of $M$ iron ore reduction factories. In each of these reducing factories the mineral is proccesed, producing a set $J = \left \{ 1,2, ..., j, ..., N \right \} $ of $N$ types of different iron ingots. These ingots are sent to a set $K = \left \{ 1,2, ..., k, ..., R\right \}$ of $R$ producing factories, each of which produces a set $L = \left \{ 1,2, ..., l, ..., P\right \}$ of $P$ different products. Suppose the following is known:
One ton of iron processed in the reduction factory $i$ produces $a_{ij}$ tons of ingots type $j$, $\forall i\in I$, $\forall j \in J$.
From one ton of type $j$ ingots, $b_{jlk}$ tons of product $I$ are produced at production factory $k$, $\forall j \in J$, $\forall l \in L$, $\forall k \in K$.
The maximum number of tons of ingots that can be produced in the reduction factory $i$ is $C_i$, $\forall i \in I$.
The maximum number of tons of ingots (of all types) that can be process at production factory $k$ is $U_k$, $\forall k \in K$.
The required quantity of tons of product type $l$ is $D_l$, $ \forall l \in L$.
The total tonnes of ingots processed by the fabrication factories must be equal to the number of tons of ingots sent by the reduction factories.
I need to do a linear programming model that allows the manufacturing company plan its production conveniently. Considering $M = 2$; $N = 5$; $R = 3$; $P = 4$.
