## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ = number of luxury tickets
- $x_2$ = number of regular tickets

The objective function is to maximize profit: $500x_1 + 300x_2$

The constraints are:
1. The cruise ship can carry at most 500 passengers: $x_1 + x_2 \leq 500$
2. The cruise ship reserves at least 100 luxury tickets: $x_1 \geq 100$
3. At least 2 times as many passengers prefer to buy regular tickets than luxury tickets: $x_2 \geq 2x_1$

## Step 2: Convert the problem into a Gurobi-compatible format

The symbolic representation is as follows:
```json
{
    'sym_variables': [('x1', 'luxury tickets'), ('x2', 'regular tickets')],
    'objective_function': '500*x1 + 300*x2',
    'constraints': [
        'x1 + x2 <= 500',
        'x1 >= 100',
        'x2 >= 2*x1'
    ]
}
```

## Step 3: Write the Gurobi code to solve the optimization problem

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="luxury_tickets")
    x2 = model.addVar(lb=0, name="regular_tickets")

    # Set the objective function
    model.setObjective(500 * x1 + 300 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 + x2 <= 500, name="total_passengers")
    model.addConstr(x1 >= 100, name="min_luxury_tickets")
    model.addConstr(x2 >= 2 * x1, name="regular_to_luxury_ratio")

    # Update the model
    model.update()

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of luxury tickets: {x1.varValue}")
        print(f"Number of regular tickets: {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_cruise_ship_problem()
```