To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

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 a profit of $50 is made on each premium ticket and a profit of $30 is made on each regular ticket, the objective function can be written as:
\[ \text{Maximize} \quad 50x_1 + 30x_2 \]

Now, let's consider the constraints:
1. The Ferris wheel can take at most 250 people: \( x_1 + x_2 \leq 250 \).
2. There are a minimum of 50 premium tickets available: \( x_1 \geq 50 \).
3. At least 3 times as many people prefer to buy regular tickets than premium tickets: \( x_2 \geq 3x_1 \).

Non-negativity constraints also apply since the number of tickets cannot be negative:
- \( x_1 \geq 0 \),
- \( x_2 \geq 0 \).

Thus, the symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of premium tickets sold'), ('x2', 'number of regular tickets sold')],
    'objective_function': '50*x1 + 30*x2',
    'constraints': [
        'x1 + x2 <= 250',
        'x1 >= 50',
        'x2 >= 3*x1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this optimization problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

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

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

# Add constraints
m.addConstr(x1 + x2 <= 250, "total_capacity")
m.addConstr(x1 >= 50, "min_premium_tickets")
m.addConstr(x2 >= 3*x1, "regular_vs_premium")

# 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")
```