## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, and then list the constraints.

### Variables
- $x_1$: Number of race cars produced
- $x_2$: Number of regular cars produced

### Objective Function
The objective is to maximize profit. Given that the profit per race car is $20000 and the profit per regular car is $10000, the objective function can be written as:
\[ \text{Maximize:} \quad 20000x_1 + 10000x_2 \]

### Constraints
1. The race car team can make at most 3 race cars per day: $x_1 \leq 3$
2. The regular car team can make at most 5 regular cars per day: $x_2 \leq 5$
3. At most 6 cars of either type can be safety checked per day: $x_1 + x_2 \leq 6$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'race cars'), ('x2', 'regular cars')],
    'objective_function': '20000*x1 + 10000*x2',
    'constraints': [
        'x1 <= 3',
        'x2 <= 5',
        'x1 + x2 <= 6',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="race_cars", lb=0, ub=3, vtype=gp.GRB.INTEGER)  # Number of race cars
x2 = model.addVar(name="regular_cars", lb=0, ub=5, vtype=gp.GRB.INTEGER)  # Number of regular cars

# Objective function: Maximize profit
model.setObjective(20000*x1 + 10000*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 <= 3, name="race_car_limit")
model.addConstr(x2 <= 5, name="regular_car_limit")
model.addConstr(x1 + x2 <= 6, name="safety_check_limit")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {model.getVarByName('race_cars').varValue} race cars, {model.getVarByName('regular_cars').varValue} regular cars")
    print(f"Maximum profit: ${model.objVal}")
else:
    print("No optimal solution found")
```