## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The objective function to be minimized is:

\[ 3 \times \text{automatic alerts} + 4 \times \text{security engineers} + 3 \times \text{network administrators} \]

The constraints are:

1. **Power consumption of automatic alerts**: \(15 \times \text{automatic alerts}\)
2. **Power consumption of security engineers**: \(1 \times \text{security engineers}\)
3. **Power consumption of network administrators**: \(19 \times \text{network administrators}\)
4. **Minimum power consumption of security engineers and network administrators**: \(1 \times \text{security engineers} + 19 \times \text{network administrators} \geq 41\)
5. **Minimum power consumption of automatic alerts and security engineers**: \(15 \times \text{automatic alerts} + 1 \times \text{security engineers} \geq 53\)
6. **Minimum total power consumption**: \(15 \times \text{automatic alerts} + 1 \times \text{security engineers} + 19 \times \text{network administrators} \geq 40\)
7. **Alternative minimum total power consumption**: This is essentially the same as constraint 6, so it is not included separately.
8. **Constraint on security engineers and network administrators**: \(-2 \times \text{security engineers} + 10 \times \text{network administrators} \geq 0\)
9. **Variable integrality constraints**: \(\text{automatic alerts}, \text{security engineers}, \text{network administrators}\) must be non-negative integers.

## Gurobi Code Formulation

```python
import gurobipy as gp

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

# Define the variables
automatic_alerts = m.addVar(name="automatic_alerts", integer=True)
security_engineers = m.addVar(name="security_engineers", integer=True)
network_administrators = m.addVar(name="network_administrators", integer=True)

# Objective function
m.setObjective(3 * automatic_alerts + 4 * security_engineers + 3 * network_administrators, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(automatic_alerts * 15 + security_engineers * 1 + network_administrators * 19 <= 234, name="power_consumption_limit")
m.addConstr(security_engineers * 1 + network_administrators * 19 >= 41, name="min_security_engineers_network_administrators_power")
m.addConstr(automatic_alerts * 15 + security_engineers * 1 >= 53, name="min_automatic_alerts_security_engineers_power")
m.addConstr(automatic_alerts * 15 + security_engineers * 1 + network_administrators * 19 >= 40, name="min_total_power_consumption")
m.addConstr(-2 * security_engineers + 10 * network_administrators >= 0, name="security_engineers_network_administrators_constraint")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Automatic Alerts: {automatic_alerts.varValue}")
    print(f"Security Engineers: {security_engineers.varValue}")
    print(f"Network Administrators: {network_administrators.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```