## Symbolic Representation

The problem can be converted into a symbolic representation as follows:

Let's define the variables:
- $x_1$: Number of SUV cars produced
- $x_2$: Number of minivans produced

The objective function is to maximize profit:
Maximize: $7500x_1 + 4000x_2$

The constraints are:
1. The SUV car factory can make at most 5 SUV cars per day: $x_1 \leq 5$
2. The minivan car factory can make at most 3 minivans per day: $x_2 \leq 3$
3. The third-party finishing touches can process at most 5 vehicles of either type per day: $x_1 + x_2 \leq 5$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'SUV cars'), ('x2', 'minivans')],
    'objective_function': '7500*x1 + 4000*x2',
    'constraints': [
        'x1 <= 5',
        'x2 <= 3',
        'x1 + x2 <= 5',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, ub=5, name="SUV_cars")
    x2 = model.addVar(lb=0, ub=3, name="minivans")

    # Define the objective function
    model.setObjective(7500 * x1 + 4000 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 <= 5, name="SUV_factory_constraint")
    model.addConstr(x2 <= 3, name="minivan_factory_constraint")
    model.addConstr(x1 + x2 <= 5, name="finishing_touches_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of SUV cars to produce: {x1.varValue}")
        print(f"Number of minivans to produce: {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```