To solve the given problem, let's first break down the natural language description into a symbolic representation. This involves defining variables and translating the objective function and constraints into algebraic terms.

Let:
- \(x_1\) represent the number of cushioned seats.
- \(x_2\) represent the number of regular seats.

The objective function aims to maximize profit. Given that a profit of $30 is made on each cushioned seat and $10 on each regular seat, the objective function can be represented as:
\[ \text{Maximize: } 30x_1 + 10x_2 \]

The constraints are as follows:
1. The total number of seats (cushioned and regular) cannot exceed 150.
\[ x_1 + x_2 \leq 150 \]
2. At least 50 seats must be cushioned.
\[ x_1 \geq 50 \]
3. At least twice as many people prefer to travel by regular seats than by cushioned seats.
\[ x_2 \geq 2x_1 \]

Now, let's represent this problem in the required JSON format:

```json
{
    'sym_variables': [('x1', 'number of cushioned seats'), ('x2', 'number of regular seats')],
    'objective_function': '30*x1 + 10*x2',
    'constraints': ['x1 + x2 <= 150', 'x1 >= 50', 'x2 >= 2*x1']
}
```

Given this symbolic representation, we can now implement the solution using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="cushioned_seats")
x2 = m.addVar(vtype=GRB.INTEGER, name="regular_seats")

# Set the objective function
m.setObjective(30*x1 + 10*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 150, "total_seats")
m.addConstr(x1 >= 50, "min_cushioned_seats")
m.addConstr(x2 >= 2*x1, "regular_vs_cushioned")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Cushioned seats: {x1.x}")
    print(f"Regular seats: {x2.x}")
    print(f"Maximum profit: ${30*x1.x + 10*x2.x}")
else:
    print("No optimal solution found")
```