## Problem Description and Formulation

The problem is an optimization problem with integer and non-negative variables. The goal is to minimize an objective function subject to several constraints.

### Variables

- `security engineers` (integer)
- `automatic alerts` (integer)
- `patches per day` (integer)

### Objective Function

Minimize: $3 \cdot (\text{security engineers})^2 + 3 \cdot (\text{security engineers}) \cdot (\text{patches per day}) + 3 \cdot (\text{automatic alerts})^2 + 3 \cdot (\text{automatic alerts}) \cdot (\text{patches per day}) + 2 \cdot (\text{patches per day})^2 + 6 \cdot (\text{automatic alerts})$

### Constraints

1. Data confidentiality impact of security engineers: $10$
2. Data confidentiality impact of automatic alerts: $23$
3. Data confidentiality impact of patches per day: $1$
4. Total data confidentiality impact from security engineers and automatic alerts: $10 + 23 \cdot (\text{automatic alerts}) \geq 21$
5. Total combined data confidentiality impact from security engineers squared and patches per day squared: $(10)^2 + (1)^2 \cdot (\text{patches per day})^2 \geq 35$
6. Total combined data confidentiality impact: $10 + 23 \cdot (\text{automatic alerts}) + 1 \cdot (\text{patches per day}) \geq 35$
7. $10 \cdot (\text{security engineers}) - 1 \cdot (\text{patches per day}) \geq 0$

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    security_engineers = model.addVar(name="security_engineers", vtype=gurobi.GRB.INTEGER)
    automatic_alerts = model.addVar(name="automatic_alerts", vtype=gurobi.GRB.INTEGER)
    patches_per_day = model.addVar(name="patches_per_day", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(3 * security_engineers ** 2 + 3 * security_engineers * patches_per_day + 
                       3 * automatic_alerts ** 2 + 3 * automatic_alerts * patches_per_day + 
                       2 * patches_per_day ** 2 + 6 * automatic_alerts, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 + 23 * automatic_alerts >= 21, name="data_confidentiality_impact_alerts")
    model.addConstr(10 ** 2 + patches_per_day ** 2 >= 35, name="data_confidentiality_impact_squared")
    model.addConstr(10 + 23 * automatic_alerts + patches_per_day >= 35, name="total_data_confidentiality_impact")
    model.addConstr(10 * security_engineers - patches_per_day >= 0, name="security_engineers_patches_impact")

    # Non-negativity constraints (implicit for integer variables)

    # Solve the model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Security Engineers: {security_engineers.varValue}")
        print(f"Automatic Alerts: {automatic_alerts.varValue}")
        print(f"Patches per Day: {patches_per_day.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```