To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote the number of cars as \(x\) and the number of trucks as \(y\).

The objective is to maximize profit. The profit per car sold is $2000, and the profit per truck sold is $4000. Therefore, the total profit can be represented as \(2000x + 4000y\).

We have two main constraints:
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. This constraint can be written as \(30x + 45y \leq 450\).
2. **Capital Constraint**: The dealership wants to spend at most $800,000. Each car costs $30,000, and each truck costs $40,000. This constraint can be represented as \(30000x + 40000y \leq 800000\).

Additionally, there's a constraint related to the proportion of cars in stock: at least 60% of all items in stock must be cars. Mathematically, this is represented as \(x \geq 0.6(x + y)\), which simplifies to \(x \geq 1.5y\), or equivalently, \(1.5y - x \leq 0\) for linear programming purposes.

Lastly, \(x\) and \(y\) must be non-negative integers since they represent quantities of cars and trucks.

Given these constraints and the objective function, we aim to find the values of \(x\) and \(y\) that maximize profit while satisfying all constraints.

```python
from gurobipy import *

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

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

# Objective function: Maximize profit
m.setObjective(2000*x + 4000*y, GRB.MAXIMIZE)

# Constraints
m.addConstr(30*x + 45*y <= 450, "space_constraint")
m.addConstr(30000*x + 40000*y <= 800000, "capital_constraint")
m.addConstr(x >= 1.5*y, "car_proportion_constraint")
m.addConstr(x >= 0, "non_negative_cars")
m.addConstr(y >= 0, "non_negative_trucks")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: x = {x.x}, y = {y.x}")
    print(f"Maximum profit: ${2000*x.x + 4000*y.x:.2f}")
else:
    print("No optimal solution found.")
```