Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of units of Kommand to stock daily.
* `y`: Number of units of Kontrol to stock daily.

**Objective Function:**

Minimize the total cost:

```
Minimize: 11x + 3y 
```

**Constraints:**

* **Budget Constraint:** The total cost of purchasing the games cannot exceed $500.
   ```
   14x + 8y <= 500
   ```

* **Customer Attraction Constraint:** The total number of customers attracted must be at least 200.
   ```
   20x + 5y >= 200
   ```

* **Non-negativity Constraints:** The number of units stocked cannot be negative.
   ```
   x >= 0
   y >= 0
   ```


```python
from gurobipy import Model, GRB

# Create a new model
model = Model("GameShopOptimization")

# Create decision variables
x = model.addVar(vtype=GRB.INTEGER, name="Kommand")  # Kommand units, integer
y = model.addVar(vtype=GRB.INTEGER, name="Kontrol")  # Kontrol units, integer


# Set objective function
model.setObjective(11*x + 3*y, GRB.MINIMIZE)

# Add constraints
model.addConstr(14*x + 8*y <= 500, "Budget")
model.addConstr(20*x + 5*y >= 200, "Customers")


# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of Kommand units (x): {x.x}")
    print(f"Number of Kontrol units (y): {y.x}")
    print(f"Minimum Cost: {model.objVal}")
elif model.status == GRB.INFEASIBLE:
    print("Model is infeasible. No solution exists.")
else:
    print(f"Optimization terminated with status: {model.status}")

```
