## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of sleeper class tickets sold
- $x_2$ as the number of regular tickets sold

The objective is to maximize profit, which is $500x_1 + 200x_2$.

## Step 2: Translate the natural language description into semi-algebraic constraints

1. The TrainAcrossCanada can host up to 400 passengers: $x_1 + x_2 \leq 400$
2. More than 5 times as many passengers prefer to travel by regular seating than by sleeper class: $x_2 > 5x_1$
3. There are at least 50 seats reserved for sleeper class passengers: $x_1 \geq 50$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

However, to accurately represent "more than 5 times as many passengers prefer to travel by regular seating than by sleeper class," we should write it as $x_2 \geq 5x_1$ since the preference directly translates to the number of tickets.

## 3: Correct and complete the symbolic representation

The correct symbolic representation is:
- Variables: $x_1$ (sleeper class tickets), $x_2$ (regular tickets)
- Objective function: $500x_1 + 200x_2$
- Constraints:
  1. $x_1 + x_2 \leq 400$
  2. $x_2 \geq 5x_1$
  3. $x_1 \geq 50$
  4. $x_1, x_2 \geq 0$

## 4: Express the problem in the required JSON format

```json
{
  'sym_variables': [('x1', 'sleeper class tickets'), ('x2', 'regular tickets')],
  'objective_function': '500*x1 + 200*x2',
  'constraints': [
    'x1 + x2 <= 400',
    'x2 >= 5*x1',
    'x1 >= 50',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

## 5: Implement the problem in Gurobi Python

```python
import gurobi

def train_across_canada():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="sleeper_class", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="regular_class", lb=0, ub=gurobi.GRB.INFINITY)

    # Objective function
    model.setObjective(500 * x1 + 200 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 400, name="total_passengers")
    model.addConstr(x2 >= 5 * x1, name="regular_to_sleeper_ratio")
    model.addConstr(x1 >= 50, name="sleeper_class_min")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum profit: ${500*x1.varValue + 200*x2.varValue}")
    else:
        print("No optimal solution found")

train_across_canada()
```