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

Let's define the symbolic variables:
- $x_1$ represents the number of guided tickets sold.
- $x_2$ represents the number of regular tickets sold.

The objective function to maximize profit is: $50x_1 + 20x_2$.

The constraints based on the problem description are:
1. The museum can sell at most 300 tickets: $x_1 + x_2 \leq 300$.
2. The museum reserves at least 50 tickets to be guided: $x_1 \geq 50$.
3. At least 3 times as many people prefer to buy regular tickets than guided tickets: $x_2 \geq 3x_1$.
4. Non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$. However, since $x_1 \geq 50$, the $x_1 \geq 0$ constraint is implicitly satisfied.

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

The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'guided tickets'), ('x2', 'regular tickets')],
    'objective_function': '50*x1 + 20*x2',
    'constraints': [
        'x1 + x2 <= 300',
        'x1 >= 50',
        'x2 >= 3*x1'
    ]
}
```

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

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='guided_tickets', lb=0, ub=300, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='regular_tickets', lb=0, ub=300, vtype=gurobi.GRB.INTEGER)

    # Objective function: maximize 50*x1 + 20*x2
    model.setObjective(50*x1 + 20*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 300, name='total_tickets')
    model.addConstr(x1 >= 50, name='min_guided_tickets')
    model.addConstr(x2 >= 3*x1, name='regular_to_guided_ratio')

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: guided tickets = {x1.varValue}, regular tickets = {x2.varValue}")
    else:
        print("The model is infeasible")

solve_museum_ticket_problem()
```