A company must allocate oil produced from their two plants to meet all the demands of two markets. The cost per litre of allocation from plant \( i \in \{1,2\} \) to market \( j \in \{1,2\} \) is denoted by \( C_{ij} \). The market demand \( D_j \), plant production capacity \( K_i \) and \( C_{ij} \) values are given in the table.
| Market 1 (j = 1) | Market 2 (j = 2) | Capacity \( K_i \) (litres) |
|---|
| Plant 1 (i = 1) | \( C_{11} = 250 \) | \( C_{12} = 280 \) | \( K_1 = 500 \) |
| Plant 2 (i = 2) | \( C_{21} = 150 \) | \( C_{22} = 180 \) | \( K_2 = 600 \) |
| Demand \( D_j \) (litres) | \( D_1 = 300 \) | \( D_2 = 400 \) | |
The company hired an intern to formulate an optimization model to decide on the quantity (\( X_{ij} \)) to be allocated from plant \( i \) to market \( j \), and the formulation is given below:
Minimize \( Z = \sum_{i=1}^{2} \sum_{j=1}^{2} C_{ij} X_{ij} \)
Subject to:
\( \sum_{j=1}^{2} X_{ij} \le K_i \quad \forall i \in \{1,2\} \)
\( \sum_{i=1}^{2} X_{ij} \le D_j \quad \forall j \in \{1,2\} \)
\( X_{ij} \ge 0 \)
The optimal value of the objective function of the linear programming problem formulated by the intern is ______ (in integer).