To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

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

The objective is to maximize profit, given that the profit per premium ticket is $50 and per regular ticket is $30. Thus, the objective function can be written as:
\[ \text{Maximize: } 50x_1 + 30x_2 \]

Given the constraints:
1. The total number of tickets sold is 500: $x_1 + x_2 = 500$,
2. At least 100 premium tickets are reserved: $x_1 \geq 100$,
3. At least 3 times as many people prefer regular tickets than premium tickets: $x_2 \geq 3x_1$.

Thus, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'number of premium tickets'), ('x2', 'number of regular tickets')],
  'objective_function': '50*x1 + 30*x2',
  'constraints': ['x1 + x2 = 500', 'x1 >= 100', 'x2 >= 3*x1']
}
```

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

```python
from gurobipy import *

# Create a new model
m = Model("Ticket_Sales")

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

# Set the objective function
m.setObjective(50*x1 + 30*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 == 500, "total_tickets")
m.addConstr(x1 >= 100, "premium_minimum")
m.addConstr(x2 >= 3*x1, "regular_minimum")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Premium tickets: {x1.x}")
    print(f"Regular tickets: {x2.x}")
    print(f"Total profit: ${50*x1.x + 30*x2.x}")
else:
    print("No optimal solution found")
```