## Symbolic Representation of the Optimization Problem

The optimization problem can be symbolically represented as follows:

```json
{
    'sym_variables': [
        ('x1', 'PX7 consoles'),
        ('x2', 'Silent X consoles')
    ],
    'objective_function': '40*x1 + 75*x2',
    'constraints': [
        'x1 >= 2*x2', 
        '3*x1 + 7*x2 <= 48', 
        'x1 >= 0', 
        'x2 >= 0'
    ]
}
```

## Gurobi Code for the Optimization Problem

To solve this linear programming optimization problem using Gurobi, we can use the following Python code:

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='PX7_consoles', obj=40, lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='Silent_X_consoles', obj=75, lb=0, vtype=gurobi.GRB.INTEGER)

    # Add constraints
    model.addConstr(x1 >= 2 * x2, name='PX7_SilentX_ratio')
    model.addConstr(3 * x1 + 7 * x2 <= 48, name='Labor_hours_constraint')

    # Set the model objective
    model.setObjective(x1.obj * x1 + x2.obj * x2, gurobi.GRB.MAXIMIZE)

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal production levels: {x1.x} PX7 consoles, {x2.x} Silent X consoles")
        print(f"Maximum profit: ${model.objVal:.2f}")
    else:
        print("The model is infeasible.")

solve_production_problem()
```

However, a more pythonic way, using callbacks and preserver variables at their original gurobi objects is shown below:

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='x1', obj=40, lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='x2', obj=75, lb=0, vtype=gurobi.GRB.INTEGER)

    # Add constraints
    model.addConstr(x1 >= 2 * x2, name='PX7_SilentX_ratio')
    model.addConstr(3 * x1 + 7 * x2 <= 48, name='Labor_hours_constraint')

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal production levels: {x1.x} PX7 consoles, {x2.x} Silent X consoles")
        print(f"Maximum profit: ${model.objVal:.2f}")
    else:
        print("The model is infeasible.")

solve_production_problem()
```