To solve this optimization problem, we need to maximize the profit from selling both hybrid and electric models of cars, subject to constraints on daily demand and total production capacity.

Let's denote:
- $y_1$ as the number of hybrid models made per day,
- $y_2$ as the number of electric models made per day.

The objective function (total profit) can be represented as $4500y_1 + 5500y_2$, since the profit per hybrid model is $4500 and per electric model is $5500.

Constraints are:
1. Daily demand for hybrid models: $y_1 \leq 9$
2. Daily demand for electric models: $y_2 \leq 5$
3. Total production capacity per day: $y_1 + y_2 \leq 10$
4. Non-negativity constraints: $y_1 \geq 0, y_2 \geq 0$

This problem can be formulated as a linear programming (LP) problem.

```python
from gurobipy import *

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

# Define variables
y1 = m.addVar(lb=0, name="hybrid_models")  # Number of hybrid models
y2 = m.addVar(lb=0, name="electric_models")  # Number of electric models

# Set the objective function: Maximize profit
m.setObjective(4500*y1 + 5500*y2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(y1 <= 9, "hybrid_demand")
m.addConstr(y2 <= 5, "electric_demand")
m.addConstr(y1 + y2 <= 10, "total_production")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hybrid models: {y1.x}")
    print(f"Electric models: {y2.x}")
    print(f"Total profit: ${4500*y1.x + 5500*y2.x}")
else:
    print("No optimal solution found")
```