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

Let's denote:
- $x_1$ as the number of guided tour packages sold
- $x_2$ as the number of regular tickets sold

The objective is to maximize profit. The profit per guided tour package is $500, and the profit per regular ticket is $200. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 500x_1 + 200x_2 \]

## Step 2: Define the constraints

1. The travel company can sell at most 300 tickets in total:
\[ x_1 + x_2 \leq 300 \]

2. The travel company reserves at least 50 guided tour packages:
\[ x_1 \geq 50 \]

3. At least 2 times as many people prefer to buy regular tickets than guided tour packages:
\[ x_2 \geq 2x_1 \]

4. Non-negativity constraints (number of tickets cannot be negative):
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

However, since $x_1 \geq 50$ is already specified, the non-negativity constraint for $x_1$ is implicitly satisfied.

## 3: Symbolic Representation

```json
{
    'sym_variables': [('x1', 'guided tour packages'), ('x2', 'regular tickets')],
    'objective_function': '500*x1 + 200*x2',
    'constraints': [
        'x1 + x2 <= 300',
        'x1 >= 50',
        'x2 >= 2*x1'
    ]
}
```

## 4: Gurobi Code

```python
import gurobi

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

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

    # Objective function: Maximize 500*x1 + 200*x2
    model.setObjective(500*x1 + 200*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 300, name="total_tickets")
    model.addConstr(x1 >= 50, name="min_guided_tour_packages")
    model.addConstr(x2 >= 2*x1, name="regular_tickets_vs_guided_tour_packages")

    # Update model
    model.update()

    # Solve the model
    model.optimize()

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

solve_travel_company_problem()
```