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

Let's define:
- $x_1$ as the number of monitors to keep in stock.
- $x_2$ as the number of gaming stations to keep in stock.

The objective function aims to maximize profit. Given that the profit per monitor sold is $40 and the profit per gaming station sold is $80, we can represent the total profit as:
\[ \text{Maximize:} \quad 40x_1 + 80x_2 \]

Now, let's define the constraints based on the problem description:

1. **Floor Space Constraint:** Each monitor requires 8 sq ft of floor space, and each gaming station requires 12 sq ft. The total available floor space is 150 sq ft.
\[ 8x_1 + 12x_2 \leq 150 \]

2. **Marketing Requirement Constraint:** At least 40% of all items in stock must be gaming stations.
\[ x_2 \geq 0.4(x_1 + x_2) \]
Simplifying, we get:
\[ x_2 \geq 0.4x_1 + 0.4x_2 \]
\[ 0.6x_2 \geq 0.4x_1 \]
\[ 1.5x_2 \geq x_1 \]

3. **Capital Constraint:** A monitor ties up $180 in capital, and a gaming station ties up $260. The maximum capital to be tied up is $4,000.
\[ 180x_1 + 260x_2 \leq 4000 \]

4. **Non-Negativity Constraints:** Since the number of monitors and gaming stations cannot be negative:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Thus, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of monitors'), ('x2', 'number of gaming stations')],
    'objective_function': '40*x1 + 80*x2',
    'constraints': [
        '8*x1 + 12*x2 <= 150',
        '1.5*x2 >= x1',
        '180*x1 + 260*x2 <= 4000',
        '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("Electronics_Store_Optimization")

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

# Set the objective function
m.setObjective(40*x1 + 80*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(8*x1 + 12*x2 <= 150, "floor_space")
m.addConstr(1.5*x2 >= x1, "marketing_requirement")
m.addConstr(180*x1 + 260*x2 <= 4000, "capital")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: monitors = {x1.x}, gaming_stations = {x2.x}")
    print(f"Maximum profit: ${40*x1.x + 80*x2.x}")
else:
    print("No optimal solution found")
```