Let's break down the problem using the Goal-Oriented Management Process (GOMP): 1. **Objective Function:** The objective is to minimize the combined distribution and fixed operating costs. 2. **Decision Variables:** - \( x_{ij} \): Tons of yogurt shipped from plant \( i \) to distribution center \( j \). - \( y_i \): Binary decision variable indicating whether plant \( i \) is operating (1) or not (0). 3. **Constraints:** - **Demand Constraint:** The total yogurt shipped from each plant to each distribution center must meet the demand. - **Capacity Constraint:** The total yogurt shipped from each plant cannot exceed its capacity. - **Operating Constraint:** If a plant is operating, at least one ton of yogurt must be shipped from that plant. 4. **Optimal Decisions:** - Determine the optimal values for \( x_{ij} \) and \( y_i \) that minimize the combined distribution and fixed operating costs. Let's set up the mathematical model: **Minimize:** \[ \text{Total Cost} = \sum_{i} \sum_{j} (C_{ij} \cdot x_{ij}) \sum_{i} (F_i \cdot y_i) \] **Subject to:** 1. Demand constraint: \[ \sum_{i} x_{ij} = D_j \quad \forall j \] 2. Capacity constraint: \[ \sum_{j} x_{ij} \leq R_i \cdot y_i \quad \forall i \] 3. Operating constraint: \[ y_i