Here's the formulation of the Linear Program (LP) and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of monitors in stock
* `y`: Number of gaming stations in stock

**Objective Function:**

Maximize profit: `40x + 80y`

**Constraints:**

* **Space Constraint:** `8x + 12y <= 150` (Total floor space used must be less than or equal to available space)
* **Marketing Constraint:** `y >= 0.4(x + y)` (At least 40% of items must be gaming stations)  This simplifies to `0.6y - 0.4x >= 0` or `3y - 2x >= 0`
* **Capital Constraint:** `180x + 260y <= 4000` (Total capital tied up must be less than or equal to the available capital)
* **Non-negativity Constraints:** `x >= 0`, `y >= 0` (Number of monitors and gaming stations cannot be negative)


```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
m = gp.Model("electronics_stock")

# Create decision variables
x = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="monitors") # Number of monitors
y = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="gaming_stations") # Number of gaming stations

# Set objective function
m.setObjective(40*x + 80*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(8*x + 12*y <= 150, "space_constraint")
m.addConstr(3*y - 2*x >= 0, "marketing_constraint")
m.addConstr(180*x + 260*y <= 4000, "capital_constraint")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Profit: ${m.objVal:.2f}")
    print(f"Number of Monitors: {x.x:.2f}")
    print(f"Number of Gaming Stations: {y.x:.2f}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
