To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of days farm 1 operates
- $x_2$ as the number of days farm 2 operates

The objective function is to minimize the total cost, which can be represented as:
\[500x_1 + 400x_2\]

The constraints are based on the yield of each fruit and the demand for them:
- For apples: $10x_1 + 7x_2 \geq 50$
- For oranges: $15x_1 + 8x_2 \geq 60$
- For pears: $5x_1 + 9x_2 \geq 55$

Additionally, since the number of days cannot be negative, we have:
- $x_1 \geq 0$
- $x_2 \geq 0$

The symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of days farm 1 operates'), ('x2', 'number of days farm 2 operates')],
    'objective_function': '500*x1 + 400*x2',
    'constraints': [
        '10*x1 + 7*x2 >= 50',
        '15*x1 + 8*x2 >= 60',
        '5*x1 + 9*x2 >= 55',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Fruit_Farm_Optimization")

# Define the variables
x1 = m.addVar(name='x1', lb=0)
x2 = m.addVar(name='x2', lb=0)

# Set the objective function
m.setObjective(500*x1 + 400*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(10*x1 + 7*x2 >= 50, name='apples_constraint')
m.addConstr(15*x1 + 8*x2 >= 60, name='oranges_constraint')
m.addConstr(5*x1 + 9*x2 >= 55, name='pears_constraint')

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found: x1 = {x1.x}, x2 = {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```