## Problem Description and Symbolic Representation

The problem involves a car dealership that wants to stock cars and trucks to maximize profit, given certain constraints on space and capital.

### Symbolic Variables
- $x_1$ : Number of cars
- $x_2$ : Number of trucks

### Objective Function
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 represented as:
\[ \text{Maximize:} \quad 2000x_1 + 4000x_2 \]

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

2. **Product Mix Constraint**: The dealership wants a minimum of 60% of all items in stock to be cars.
\[ x_1 \geq 0.6(x_1 + x_2) \]
\[ 0.4x_1 \geq 0.6x_2 \]
\[ 0.4x_1 - 0.6x_2 \geq 0 \]
Or more simply:
\[ x_1 \geq 1.5x_2 \]

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 Constraint**: 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', 'cars'), ('x2', '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'
    ]
}
```

## Gurobi Code in Python
```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="cars", lb=0, vtype=gp.GRB.INTEGER)  # Number of cars
x2 = model.addVar(name="trucks", lb=0, vtype=gp.GRB.INTEGER)  # Number of trucks

# Objective function: Maximize profit
model.setObjective(2000*x1 + 4000*x2, gp.GRB.MAXIMIZE)

# Space constraint
model.addConstr(30*x1 + 45*x2 <= 450, name="Space_Constraint")

# Product mix constraint
model.addConstr(x1 >= 1.5*x2, name="Product_Mix_Constraint")

# Capital constraint
model.addConstr(30000*x1 + 40000*x2 <= 800000, name="Capital_Constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal number of cars: {x1.varValue}")
    print(f"Optimal number of trucks: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("The model is infeasible.")
```