To solve the given optimization problem, we first need to define the variables and the objective function symbolically, followed by translating these into Gurobi code in Python.

### Symbolic Representation:

Let's denote:
- \(x_1\) as the number of first-class seats.
- \(x_2\) as the number of regular seats.

The objective function is to maximize profit. Given that a profit of $1200 is made on each first-class seat and $700 on each regular seat, the objective function can be written as:
\[ \text{Maximize: } 1200x_1 + 700x_2 \]

The constraints based on the problem description are:
1. The total number of seats is 300: \( x_1 + x_2 = 300 \)
2. At least 50 seats must be first-class: \( x_1 \geq 50 \)
3. At least three times as many people prefer regular seats to first-class seats: \( x_2 \geq 3x_1 \)

### Symbolic Representation in JSON Format:
```json
{
  'sym_variables': [('x1', 'number of first-class seats'), ('x2', 'number of regular seats')],
  'objective_function': '1200*x1 + 700*x2',
  'constraints': ['x1 + x2 = 300', 'x1 >= 50', 'x2 >= 3*x1']
}
```

### Gurobi Code in Python:
To solve this linear programming problem using Gurobi, we'll write the following Python code:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(1200*x1 + 700*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 == 300, name='total_seats')
m.addConstr(x1 >= 50, name='min_first_class')
m.addConstr(x2 >= 3*x1, name='regular_vs_first_class')

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found.")
    print(f"Number of first-class seats: {x1.x}")
    print(f"Number of regular seats: {x2.x}")
    print(f"Maximum profit: ${1200*x1.x + 700*x2.x}")
else:
    print("No optimal solution found.")

```