To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's define:
- $x_1$ as the number of PX7 consoles produced.
- $x_2$ as the number of Silent X consoles produced.

The objective is to maximize profit. Given that one PX7 console yields a $40 profit and one Silent X console yields a $75 profit, the objective function can be written as:
\[ \text{Maximize:} \quad 40x_1 + 75x_2 \]

Now, let's consider the constraints:

1. **Labor Constraint:** The business can spend up to 48 hours a week. Since one PX7 console requires 3 hours of labor and one Silent X console requires 7 hours of labor, we have:
\[ 3x_1 + 7x_2 \leq 48 \]

2. **Demand Forecast Constraint:** The business decides to produce at least twice as many PX7 consoles as Silent X ones:
\[ x_1 \geq 2x_2 \]

3. **Non-Negativity Constraints:** Since the number of consoles produced cannot be negative, we also have:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

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

To solve this problem using Gurobi in Python, we can use the following code:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="px7_consoles", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="silent_x_consoles", lb=0)

# Set the objective function
m.setObjective(40*x1 + 75*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 + 7*x2 <= 48, "labor_constraint")
m.addConstr(x1 >= 2*x2, "demand_forecast_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of PX7 consoles: {x1.x}")
    print(f"Number of Silent X consoles: {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```