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.

### Symbolic Representation:

Let's define:
- $x_1$ as the number of race cars produced.
- $x_2$ as the number of regular cars produced.

The objective is to maximize profit. Given that the profit per race car is $20,000 and per regular car is $10,000, the objective function can be written as:
\[ \text{Maximize:} \quad 20000x_1 + 10000x_2 \]

Constraints based on production capacities and safety checks are:
1. The race car team can produce at most 3 race cars per day: $x_1 \leq 3$
2. The regular car team can produce at most 5 regular cars per day: $x_2 \leq 5$
3. At most 6 cars of either type can be safety checked in a day: $x_1 + x_2 \leq 6$

Non-negativity constraints (since production cannot be negative):
- $x_1 \geq 0$
- $x_2 \geq 0$

### Symbolic Representation in JSON Format:

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

### Gurobi Code in Python:

To solve this linear programming problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="race_cars", lb=0)
x2 = m.addVar(vtype=GRB.INTEGER, name="regular_cars", lb=0)

# Set objective function
m.setObjective(20000*x1 + 10000*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 3, "race_car_production_limit")
m.addConstr(x2 <= 5, "regular_car_production_limit")
m.addConstr(x1 + x2 <= 6, "safety_check_limit")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of race cars: {x1.x}")
    print(f"Number of regular cars: {x2.x}")
    print(f"Total profit: ${20000*x1.x + 10000*x2.x}")
else:
    print("No optimal solution found")
```