## Optimization Problem Formulation

The problem is a mixed-integer linear programming (MILP) problem. We will use the Gurobi library to solve it.

### Variables

* `patches_per_day`: integer
* `intrusion_analysts`: integer
* `security_engineers`: integer
* `system_administrators`: integer

### Objective Function

Minimize: `7 * patches_per_day + 6 * intrusion_analysts + 5 * security_engineers + 4 * system_administrators`

### Constraints

The constraints can be grouped into several categories:

#### Resource Constraints

* Network Latency:
	+ `20 * patches_per_day + 14 * intrusion_analysts + 2 * security_engineers + 14 * system_administrators <= 313`
	+ `20 * patches_per_day + 14 * intrusion_analysts >= 40`
	+ `20 * patches_per_day + 14 * system_administrators >= 58`
	+ `14 * intrusion_analysts + 2 * security_engineers + 14 * system_administrators >= 57`
	+ `20 * patches_per_day + 14 * intrusion_analysts + 2 * security_engineers + 14 * system_administrators >= 57`
	+ `20 * patches_per_day + 2 * security_engineers <= 265`
	+ `14 * intrusion_analysts + 2 * security_engineers <= 145`
	+ `20 * patches_per_day + 14 * intrusion_analysts <= 79`
	+ `20 * patches_per_day + 14 * system_administrators <= 97`
	+ `20 * patches_per_day + 14 * intrusion_analysts + 14 * system_administrators <= 262`
* Data Confidentiality Impact:
	+ `5 * intrusion_analysts + 8 * system_administrators >= 51`
	+ `5 * patches_per_day + 5 * intrusion_analysts + 21 * security_engineers + 8 * system_administrators >= 51`
	+ `5 * intrusion_analysts + 21 * security_engineers + 8 * system_administrators <= 279`
* Power Consumption:
	+ `18 * patches_per_day + 15 * intrusion_analysts + 14 * security_engineers + 5 * system_administrators <= 259`
	+ `14 * security_engineers + 5 * system_administrators >= 63`
	+ `15 * intrusion_analysts + 14 * security_engineers >= 60`
	+ `18 * patches_per_day + 5 * system_administrators >= 62`
	+ `15 * intrusion_analysts + 5 * system_administrators >= 61`
	+ `18 * patches_per_day + 14 * security_engineers >= 51`
	+ `18 * patches_per_day + 15 * intrusion_analysts >= 49`
	+ `18 * patches_per_day + 15 * intrusion_analysts + 14 * security_engineers + 5 * system_administrators >= 49`
	+ `15 * intrusion_analysts + 14 * system_administrators <= 96`

#### Additional Constraints

* `10 * patches_per_day - 5 * security_engineers >= 0`
* `-security_engineers + 9 * system_administrators >= 0`

### Gurobi Code

```python
import gurobi

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

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

    # Objective function
    model.setObjective(7 * patches_per_day + 6 * intrusion_analysts + 5 * security_engineers + 4 * system_administrators, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(20 * patches_per_day + 14 * intrusion_analysts + 2 * security_engineers + 14 * system_administrators <= 313)
    model.addConstr(20 * patches_per_day + 14 * intrusion_analysts >= 40)
    model.addConstr(20 * patches_per_day + 14 * system_administrators >= 58)
    model.addConstr(14 * intrusion_analysts + 2 * security_engineers + 14 * system_administrators >= 57)
    model.addConstr(20 * patches_per_day + 14 * intrusion_analysts + 2 * security_engineers + 14 * system_administrators >= 57)
    model.addConstr(20 * patches_per_day + 2 * security_engineers <= 265)
    model.addConstr(14 * intrusion_analysts + 2 * security_engineers <= 145)
    model.addConstr(20 * patches_per_day + 14 * intrusion_analysts <= 79)
    model.addConstr(20 * patches_per_day + 14 * system_administrators <= 97)
    model.addConstr(20 * patches_per_day + 14 * intrusion_analysts + 14 * system_administrators <= 262)

    model.addConstr(5 * intrusion_analysts + 8 * system_administrators >= 51)
    model.addConstr(5 * patches_per_day + 5 * intrusion_analysts + 21 * security_engineers + 8 * system_administrators >= 51)
    model.addConstr(5 * intrusion_analysts + 21 * security_engineers + 8 * system_administrators <= 279)

    model.addConstr(18 * patches_per_day + 15 * intrusion_analysts + 14 * security_engineers + 5 * system_administrators <= 259)
    model.addConstr(14 * security_engineers + 5 * system_administrators >= 63)
    model.addConstr(15 * intrusion_analysts + 14 * security_engineers >= 60)
    model.addConstr(18 * patches_per_day + 5 * system_administrators >= 62)
    model.addConstr(15 * intrusion_analysts + 5 * system_administrators >= 61)
    model.addConstr(18 * patches_per_day + 14 * security_engineers >= 51)
    model.addConstr(18 * patches_per_day + 15 * intrusion_analysts >= 49)
    model.addConstr(18 * patches_per_day + 15 * intrusion_analysts + 14 * security_engineers + 5 * system_administrators >= 49)
    model.addConstr(15 * intrusion_analysts + 14 * system_administrators <= 96)

    model.addConstr(10 * patches_per_day - 5 * security_engineers >= 0)
    model.addConstr(-security_engineers + 9 * system_administrators >= 0)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print("Patches per day:", patches_per_day.varValue)
        print("Intrusion analysts:", intrusion_analysts.varValue)
        print("Security engineers:", security_engineers.varValue)
        print("System administrators:", system_administrators.varValue)
        print("Objective function value:", model.objVal)
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```