## Symbolic Representation

To convert the given natural language description into a symbolic representation, let's define the variables and the objective function, as well as the constraints.

### Variables
- $x_1$: Days per week the eastern location operates
- $x_2$: Days per week the western location operates

### Objective Function
The objective is to minimize the total operating cost. The eastern location costs $1000 per day, and the western location costs $2000 per day. Therefore, the objective function is:
\[ \text{Minimize:} \quad 1000x_1 + 2000x_2 \]

### Constraints
1. Cheap caviar: $5x_1 + 2x_2 \geq 25$
2. Regular caviar: $7x_1 + 6x_2 \geq 35$
3. Expensive caviar: $x_1 + 4x_2 \geq 15$
4. Non-negativity: $x_1 \geq 0, x_2 \geq 0$
5. Since $x_1$ and $x_2$ represent days, they should also be integers: $x_1 \in \mathbb{Z}, x_2 \in \mathbb{Z}$

## Gurobi Code

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Caviar_Production")

# Define variables
x1 = model.addVar(name="Eastern_Location_Days", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="Western_Location_Days", lb=0, vtype=gp.GRB.INTEGER)

# Objective function: Minimize 1000x1 + 2000x2
model.setObjective(1000*x1 + 2000*x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(5*x1 + 2*x2 >= 25, name="Cheap_Caviar_Constraint")
model.addConstr(7*x1 + 6*x2 >= 35, name="Regular_Caviar_Constraint")
model.addConstr(x1 + 4*x2 >= 15, name="Expensive_Caviar_Constraint")

# Solve the model
model.solve()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Eastern Location Days: {x1.varValue}")
    print(f"Western Location Days: {x2.varValue}")
    print(f"Objective Value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## Symbolic Representation in JSON

```json
{
  "sym_variables": [
    ["x1", "Eastern Location Days"],
    ["x2", "Western Location Days"]
  ],
  "objective_function": "1000x1 + 2000x2",
  "constraints": [
    "5x1 + 2x2 >= 25",
    "7x1 + 6x2 >= 35",
    "x1 + 4x2 >= 15",
    "x1 >= 0",
    "x2 >= 0"
  ]
}
```