## Step 1: Define the symbolic representation of the problem
Let's denote the number of first-class tickets as $x_1$ and the number of economy-class tickets as $x_2$. The profit on each first-class ticket is $150, and on each economy-class ticket is $350. The objective is to maximize the total profit.

## Step 2: Formulate the objective function
The objective function to maximize profit is $150x_1 + 350x_2$.

## 3: Identify the constraints
1. Total tickets: $x_1 + x_2 \leq 150$ (the flight has 150 tickets).
2. Minimum first-class tickets: $x_1 \geq 20$ (at least 20 tickets are reserved for first-class).
3. Economy-class vs. first-class tickets: $x_2 \geq 3x_1$ (at least 3 times as many people prefer economy-class than first-class).
4. Non-negativity: $x_1 \geq 0, x_2 \geq 0$ (number of tickets cannot be negative).

## 4: Convert the problem into a symbolic representation
```json
{
'sym_variables': [('x1', 'first-class tickets'), ('x2', 'economy-class tickets')],
'objective_function': '150*x1 + 350*x2',
'constraints': [
'x1 + x2 <= 150',
'x1 >= 20',
'x2 >= 3*x1',
'x1 >= 0',
'x2 >= 0'
]
}
```

## 5: Implement the problem in Gurobi code
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="first_class_tickets", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(lb=0, name="economy_class_tickets", vtype=gurobi.GRB.INTEGER)

    # Objective function: maximize 150*x1 + 350*x2
    model.setObjective(150*x1 + 350*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 150, name="total_tickets")
    model.addConstr(x1 >= 20, name="min_first_class")
    model.addConstr(x2 >= 3*x1, name="economy_vs_first_class")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"First-class tickets: {x1.varValue}")
        print(f"Economy-class tickets: {x2.varValue}")
        print(f"Max Profit: {150*x1.varValue + 350*x2.varValue}")
    else:
        print("No optimal solution found.")

solve_flight_ticket_problem()
```