To solve the given optimization problem, we first need to convert 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 sleeper class tickets sold,
- $x_2$ as the number of general class tickets sold.

The objective is to maximize profit. Given that a profit of $200 is made per sleeper class ticket and a profit of $80 is made per general class ticket, the objective function can be represented as:
\[ \text{Maximize: } 200x_1 + 80x_2 \]

Now, let's formulate the constraints based on the problem description:
1. The train can carry at most 400 passengers, so the total number of tickets sold cannot exceed 400:
\[ x_1 + x_2 \leq 400 \]
2. At least 50 sleeper class tickets must be reserved:
\[ x_1 \geq 50 \]
3. At least 1.5 times as many passengers prefer to buy general class tickets than sleeper class tickets:
\[ x_2 \geq 1.5x_1 \]

Additionally, we know that $x_1$ and $x_2$ must be non-negative since they represent the number of tickets.

In symbolic representation, this problem can be encapsulated as follows:

```json
{
  'sym_variables': [('x1', 'number of sleeper class tickets'), ('x2', 'number of general class tickets')],
  'objective_function': '200*x1 + 80*x2',
  'constraints': ['x1 + x2 <= 400', 'x1 >= 50', 'x2 >= 1.5*x1', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

# Create a model
m = Model("Train_Ticket_Optimization")

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

# Set objective function
m.setObjective(200*x1 + 80*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 400, "total_passengers")
m.addConstr(x1 >= 50, "minimum_sleeper_class")
m.addConstr(x2 >= 1.5*x1, "general_vs_sleeper_ratio")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Sleeper class tickets: {x1.x}")
    print(f"General class tickets: {x2.x}")
    print(f"Maximum profit: ${200*x1.x + 80*x2.x}")
else:
    print("No optimal solution found.")
```