To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's denote:
- $x_1$ as the number of cars to be stocked,
- $x_2$ as the number of trucks to be stocked.

The objective is to maximize profit. Given that the profit per car sold is $2000 and the profit per truck sold is $4000, the objective function can be written as:
\[ \text{Maximize: } 2000x_1 + 4000x_2 \]

Now, let's define the constraints based on the problem description:

1. **Space Constraint**: Each car takes 30 sq ft of space, and each truck takes 45 sq ft of space. The total available space is 450 sq ft.
\[ 30x_1 + 45x_2 \leq 450 \]

2. **Minimum Cars Constraint**: At least 60% of all items in stock should be cars.
\[ x_1 \geq 0.6(x_1 + x_2) \]
Simplifying, we get:
\[ x_1 \geq 0.6x_1 + 0.6x_2 \]
\[ 0.4x_1 \geq 0.6x_2 \]
\[ x_1 \geq 1.5x_2 \]

3. **Capital Constraint**: The dealership wants to spend at most $800,000. Each car costs $30,000, and each truck costs $40,000.
\[ 30000x_1 + 40000x_2 \leq 800000 \]

4. **Non-Negativity Constraints**: The number of cars and trucks cannot be negative.
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Symbolic representation in JSON format:
```json
{
    'sym_variables': [('x1', 'number of cars'), ('x2', 'number of trucks')],
    'objective_function': '2000*x1 + 4000*x2',
    'constraints': [
        '30*x1 + 45*x2 <= 450',
        'x1 >= 1.5*x2',
        '30000*x1 + 40000*x2 <= 800000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="cars")
x2 = m.addVar(vtype=GRB.INTEGER, name="trucks")

# Set the objective function
m.setObjective(2000*x1 + 4000*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(30*x1 + 45*x2 <= 450, "space_constraint")
m.addConstr(x1 >= 1.5*x2, "min_cars_constraint")
m.addConstr(30000*x1 + 40000*x2 <= 800000, "capital_constraint")
m.addConstr(x1 >= 0, "non_negativity_cars")
m.addConstr(x2 >= 0, "non_negativity_trucks")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: Cars = {x1.x}, Trucks = {x2.x}")
    print(f"Maximum Profit: ${2000*x1.x + 4000*x2.x}")
else:
    print("No optimal solution found")
```