## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of regular rooms sold.
- $x_2$ represents the number of premium rooms sold.

## Step 2: Translate the objective function into symbolic notation
The objective is to maximize profit. The profit on each regular room is $100, and on each premium room is $500. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 100x_1 + 500x_2 \]

## 3: Translate the constraints into symbolic notation
The constraints given are:
1. The hotel has 500 rooms in total: $x_1 + x_2 \leq 500$
2. At least 100 rooms are reserved for regular rooms: $x_1 \geq 100$
3. A minimum of twice as many customers prefer to stay in a premium room than stay in a regular room: $x_2 \geq 2x_1$

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

## 5: Convert the problem into Gurobi code
Now, let's convert this into Gurobi code in Python:
```python
import gurobi

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

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

    # Objective function: Maximize 100*x1 + 500*x2
    model.setObjective(100*x1 + 500*x2, gurobi.GRB.MAXIMIZE)

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

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Regular rooms: {x1.varValue}")
        print(f"Premium rooms: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_hotel_room_allocation()
```