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

- $x_1$ as the number of heated seats.
- $x_2$ as the number of regular seats.

The objective function aims to maximize profit. Given that the profit per heated seat is $20 and the profit per regular seat is $15, we can represent the objective function as:

Maximize: $20x_1 + 15x_2$

The constraints based on the problem description are:

1. The total number of seats is 100: $x_1 + x_2 \leq 100$
2. At least 15 seats are reserved to be heated: $x_1 \geq 15$
3. At least 3 times as many people prefer regular seats to heated seats: $x_2 \geq 3x_1$

Additionally, since we cannot have negative seats, we also have:

4. $x_1 \geq 0$ and $x_2 \geq 0$

Now, let's represent the problem symbolically as requested:

```json
{
  'sym_variables': [('x1', 'number of heated seats'), ('x2', 'number of regular seats')],
  'objective_function': '20*x1 + 15*x2',
  'constraints': ['x1 + x2 <= 100', 'x1 >= 15', 'x2 >= 3*x1', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(name='heated_seats', vtype=GRB.INTEGER, lb=0)
x2 = m.addVar(name='regular_seats', vtype=GRB.INTEGER, lb=0)

# Set the objective function
m.setObjective(20*x1 + 15*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, name='total_seats')
m.addConstr(x1 >= 15, name='min_heated_seats')
m.addConstr(x2 >= 3*x1, name='regular_vs_heated')

# Optimize the model
m.optimize()

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