I believe the following LP should satisfy your constraints. Please try to understand constraint (3) and tell me if this is what you wanted. I modeled it separately for each input, output, plant combination. Let's assume that you want to produce 1 barrel of gasoline at the first plant. Constraint 3 then states, that $3 \leq 4x_{00}$ and $5 \leq 4x_{10}$, so you need at least $\frac{4}{3}$ barrels of input 0 and $\frac{4}{5}$ of input 1.

DECISION VARIABLES

\begin{align} x_{ij} \end{align} Number of crude barrel $i \in I$ processed at plant $j \in J$ \begin{align} y_{kj} \end{align} Number of output barrel $k \in K$ produced at plant $j \in J$

Linear Program \begin{align} \ & \max z = 2\sum_{j \in J} y_{0j} + \sum_{j \in J} y_{1j} \; \\ \textit{S.t:}\\ \\ & \sum_{j \in J} x_{0j} \leq 10,000,000 \tag1\\ & \sum_{j \in J} x_{1j} \leq 6,000,000 \tag2\\ & ic_{ij} y_{kj} \leq oc_{jk}x_{ij} \; \forall i \in I, j \in J, k \in K \tag3\\ & x_{ij} \geq 0, \; \forall i \in I, j \in J \tag4\\ & y_{kj} \geq 0, \; \forall k \in K, j \in J \tag5 \end{align}

I believe the following LP should satisfy your constraints. Please try to understand constraint (3) and tell me if this is what you wanted. I modeled it separately for each input, output, plant combination. Let's assume that you want to produce 1 barrel of gasoline at the first plant. Constraint 3 then states, that $3 \leq 4x_{00}$ and $5 \leq 4x_{10}$, so you need at least $\frac{3}{4}$ barrels of input 0 and $\frac{5}{4}$ of input 1.

DECISION VARIABLES

\begin{align} x_{ij} \end{align} Number of crude barrel $i \in I$ processed at plant $j \in J$ \begin{align} y_{kj} \end{align} Number of output barrel $k \in K$ produced at plant $j \in J$

Linear Program \begin{align} \ & \max z = 2\sum_{j \in J} y_{0j} + \sum_{j \in J} y_{1j} \; \\ \textit{S.t:}\\ \\ & \sum_{j \in J} x_{0j} \leq 10,000,000 \tag1\\ & \sum_{j \in J} x_{1j} \leq 6,000,000 \tag2\\ & ic_{ij} y_{kj} \leq oc_{jk}x_{ij} \; \forall i \in I, j \in J, k \in K \tag3\\ & x_{ij} \geq 0, \; \forall i \in I, j \in J \tag4\\ & y_{kj} \geq 0, \; \forall k \in K, j \in J \tag5 \end{align}

I believe the following LP should satisfy your constraints. Please try to understand constraint (3) and tell me if this is what you wanted.

DECISION VARIABLES

\begin{align} x_{ij} \end{align} Number of crude barrel $i \in I$ processed at plant $j \in J$ \begin{align} y_{kj} \end{align} Number of output barrel $k \in K$ produced at plant $j \in J$

Linear Program \begin{align} \ & \max z = 2\sum_{j \in J} y_{0j} + \sum_{j \in J} y_{1j} \; \\ \textit{S.t:}\\ \\ & \sum_{j \in J} x_{0j} \leq 10,000,000 \\ & \sum_{j \in J} x_{1j} \leq 6,000,000 \\ & ic_{ij} y_{kj} \leq oc_{jk}x_{ij} \; \forall i \in I, j \in J, k \in K\\ & x_{ij} \geq 0, \; \forall i \in I, j \in J \\ & y_{kj} \geq 0, \; \forall k \in K, j \in J \end{align}

I believe the following LP should satisfy your constraints. Please try to understand constraint (3) and tell me if this is what you wanted. I modeled it separately for each input, output, plant combination. Let's assume that you want to produce 1 barrel of gasoline at the first plant. Constraint 3 then states, that $3 \leq 4x_{00}$ and $5 \leq 4x_{10}$, so you need at least $\frac{4}{3}$ barrels of input 0 and $\frac{4}{5}$ of input 1.

DECISION VARIABLES

\begin{align} x_{ij} \end{align} Number of crude barrel $i \in I$ processed at plant $j \in J$ \begin{align} y_{kj} \end{align} Number of output barrel $k \in K$ produced at plant $j \in J$

Linear Program \begin{align} \ & \max z = 2\sum_{j \in J} y_{0j} + \sum_{j \in J} y_{1j} \; \\ \textit{S.t:}\\ \\ & \sum_{j \in J} x_{0j} \leq 10,000,000 \tag1\\ & \sum_{j \in J} x_{1j} \leq 6,000,000 \tag2\\ & ic_{ij} y_{kj} \leq oc_{jk}x_{ij} \; \forall i \in I, j \in J, k \in K \tag3\\ & x_{ij} \geq 0, \; \forall i \in I, j \in J \tag4\\ & y_{kj} \geq 0, \; \forall k \in K, j \in J \tag5 \end{align}