To solve this problem, we need to convert the natural language description into a mathematical representation and then translate it into Gurobi code in Python. The goal is to maximize profit given the production and safety check constraints.

Let's denote:
- \(x\) as the number of race cars produced per day.
- \(y\) as the number of regular cars produced per day.

The objective function, which represents the total profit, can be written as:
\[ \text{Maximize} \quad 20000x + 10000y \]

Given constraints are:
1. The race car team can produce at most 3 race cars per day: \( x \leq 3 \)
2. The regular car team can produce at most 5 regular cars per day: \( y \leq 5 \)
3. At most 6 cars of either type can be safety checked per day: \( x + y \leq 6 \)

Additionally, \(x\) and \(y\) must be non-negative since they represent the number of cars.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

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

# Create variables
x = m.addVar(lb=0, vtype=GRB.INTEGER, name="race_cars")
y = m.addVar(lb=0, vtype=GRB.INTEGER, name="regular_cars")

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

# Add constraints
m.addConstr(x <= 3, "max_race_cars")
m.addConstr(y <= 5, "max_regular_cars")
m.addConstr(x + y <= 6, "max_safety_checks")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Race cars: {x.x}")
    print(f"Regular cars: {y.x}")
    print(f"Total profit: ${20000*x.x + 10000*y.x}")
else:
    print("No optimal solution found")
```