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.

Let's define:
- $x_1$ as the number of regular rooms sold,
- $x_2$ as the number of premium rooms sold.

The objective is to maximize profit, with each regular room contributing $100 to the profit and each premium room contributing $500. Thus, the objective function can be written as:
\[ \text{Maximize:} \quad 100x_1 + 500x_2 \]

The constraints are as follows:
1. The hotel has a total of 500 rooms, so $x_1 + x_2 \leq 500$.
2. At least 100 rooms must be reserved for regular rooms, so $x_1 \geq 100$.
3. A minimum of twice as many customers prefer to stay in a premium room than in a regular room, which implies $x_2 \geq 2x_1$.

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of regular rooms sold'), ('x2', 'number of premium rooms sold')],
    'objective_function': '100*x1 + 500*x2',
    'constraints': ['x1 + x2 <= 500', 'x1 >= 100', 'x2 >= 2*x1']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

# Create a model
m = Model("Hotel_Rooms")

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

# Set objective function
m.setObjective(100*x1 + 500*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 500, name="total_rooms")
m.addConstr(x1 >= 100, name="min_regular_rooms")
m.addConstr(x2 >= 2*x1, name="premium_vs_regular")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Regular rooms: {x1.x}")
    print(f"Premium rooms: {x2.x}")
    print(f"Total profit: ${100*x1.x + 500*x2.x}")
else:
    print("No optimal solution found")
```