## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables as follows:

- $y_1$ for the number of hybrid models per day
- $y_2$ for the number of electric models per day

The objective is to maximize profit. The profit per hybrid model is $4500, and the profit per electric model is $5500. Therefore, the objective function can be represented as:

Maximize: $4500y_1 + 5500y_2$

The constraints based on the given information are:

1. The daily demand for hybrid models is limited to at most 9 models: $y_1 \leq 9$
2. The daily demand for electric models is limited to at most 5 models: $y_2 \leq 5$
3. The manufacturer can make a maximum of 10 total cars a day: $y_1 + y_2 \leq 10$
4. Non-negativity constraints: $y_1 \geq 0, y_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('y1', 'hybrid models per day'), ('y2', 'electric models per day')],
    'objective_function': '4500*y1 + 5500*y2',
    'constraints': [
        'y1 <= 9',
        'y2 <= 5',
        'y1 + y2 <= 10',
        'y1 >= 0',
        'y2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

def solve_eta_auto_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    y1 = model.addVar(lb=0, name="hybrid_models")
    y2 = model.addVar(lb=0, name="electric_models")

    # Objective function: Maximize 4500*y1 + 5500*y2
    model.setObjective(4500 * y1 + 5500 * y2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(y1 <= 9, name="hybrid_demand_constraint")
    model.addConstr(y2 <= 5, name="electric_demand_constraint")
    model.addConstr(y1 + y2 <= 10, name="total_cars_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: {y1.varName} = {y1.x}, {y2.varName} = {y2.x}")
    else:
        print("No optimal solution found")

solve_eta_auto_problem()
```