To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of guided tickets sold,
- $x_2$ as the number of regular tickets sold.

The objective is to maximize profit. Given that the profit per guided ticket is $50 and the profit per regular ticket is $20, the objective function can be written as:

\[ \text{Maximize: } 50x_1 + 20x_2 \]

Now, let's consider the constraints based on the problem description:
1. The museum can sell at most 300 tickets in total, so we have:
\[ x_1 + x_2 \leq 300 \]
2. The museum reserves at least 50 tickets to be guided, thus:
\[ x_1 \geq 50 \]
3. At least 3 times as many people prefer to buy regular tickets than guided tickets, which gives us:
\[ x_2 \geq 3x_1 \]

All variables $x_1$ and $x_2$ must be non-negative since they represent the number of tickets.

The symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of guided tickets'), ('x2', 'number of regular tickets')],
    'objective_function': '50*x1 + 20*x2',
    'constraints': ['x1 + x2 <= 300', 'x1 >= 50', 'x2 >= 3*x1', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we'll use the following code:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(50*x1 + 20*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 300, name="total_tickets")
m.addConstr(x1 >= 50, name="min_guided_tickets")
m.addConstr(x2 >= 3*x1, name="regular_vs_guided")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Guided tickets: {x1.x}")
    print(f"Regular tickets: {x2.x}")
    print(f"Total profit: ${50*x1.x + 20*x2.x:.2f}")
else:
    print("No optimal solution found")
```