## Symbolic Representation

The problem can be represented symbolically as follows:

Let's define the variables:
- $x_1$ as the number of days to operate farm 1
- $x_2$ as the number of days to operate farm 2

The objective is to minimize the cost: $500x_1 + 400x_2$

The constraints are:
- $10x_1 + 7x_2 \geq 50$ (apples constraint)
- $15x_1 + 8x_2 \geq 60$ (oranges constraint)
- $5x_1 + 9x_2 \geq 55$ (pears constraint)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints)

## JSON Representation

```json
{
    'sym_variables': [('x1', 'days to operate farm 1'), ('x2', 'days to operate farm 2')],
    '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'
    ]
}
```

## Gurobi Code

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="farm1_days", lb=0)  # days to operate farm 1
x2 = model.addVar(name="farm2_days", lb=0)  # days to operate farm 2

# Define the objective function
model.setObjective(500 * x1 + 400 * x2, gp.GRB.MINIMIZE)

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

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Days to operate farm 1: {x1.varValue}")
    print(f"Days to operate farm 2: {x2.varValue}")
    print(f"Total cost: {model.objVal}")
else:
    print("No optimal solution found.")
```