## Problem Description and Formulation

The problem is an optimization problem with the goal to maximize a given objective function subject to several constraints. The variables to consider are:

- patches per day
- pen testers
- intrusion analysts

The resources/attributes are given as:

```markdown
- r0 (power consumption):
  - patches per day: 11.44 kWh
  - pen testers: 11.11 kWh
  - intrusion analysts: 14.9 kWh
  - upper bound: 84 kWh

- r1 (data integrity impact):
  - patches per day: 12.65
  - pen testers: 0.78
  - intrusion analysts: 14.19
  - upper bound: 155
```

The objective function to maximize is:

\[ 7.19 \times (\text{patches per day} \times \text{pen testers}) + 1.57 \times (\text{patches per day} \times \text{intrusion analysts}) + 2.02 \times (\text{pen testers})^2 + 3.09 \times (\text{patches per day}) + 7.49 \times (\text{pen testers}) \]

Subject to the following constraints:

1. Power consumption constraints:
   - patches per day: \(11.44 \times \text{patches per day}\)
   - pen testers: \(11.11 \times \text{pen testers}\)
   - intrusion analysts: \(14.9 \times \text{intrusion analysts}\)
   - Total power consumption: \(11.44 \times \text{patches per day} + 11.11 \times \text{pen testers} + 14.9 \times \text{intrusion analysts} \leq 84\)

2. Data integrity impact constraints:
   - patches per day and intrusion analysts: \(12.65 \times \text{patches per day} + 14.19 \times \text{intrusion analysts} \leq 69\)
   - pen testers and intrusion analysts: \(0.78 \times \text{pen testers} + 14.19 \times \text{intrusion analysts} \leq 105\)
   - patches per day and pen testers: \(12.65 \times \text{patches per day} + 0.78 \times \text{pen testers} \leq 107\)
   - patches per day, pen testers, and intrusion analysts: \(12.65 \times \text{patches per day} + 0.78 \times \text{pen testers} + 14.19 \times \text{intrusion analysts} \leq 131\)

3. Variable constraints:
   - patches per day, pen testers, and intrusion analysts must be non-negative integers.

## Gurobi Code Formulation

```python
import gurobi

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

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

    # Objective function
    model.setObjective(7.19 * patches_per_day * pen_testers + 
                       1.57 * patches_per_day * intrusion_analysts + 
                       2.02 * pen_testers ** 2 + 
                       3.09 * patches_per_day + 
                       7.49 * pen_testers, 
                       gurobi.GRB.MAXIMIZE)

    # Power consumption constraint
    model.addConstr(11.44 * patches_per_day + 
                    11.11 * pen_testers + 
                    14.9 * intrusion_analysts <= 84, 
                    name="power_consumption")

    # Data integrity impact constraints
    model.addConstr(12.65 * patches_per_day + 14.19 * intrusion_analysts <= 69, 
                    name="data_integrity_patches_intrusion")
    model.addConstr(0.78 * pen_testers + 14.19 * intrusion_analysts <= 105, 
                    name="data_integrity_pen_testers_intrusion")
    model.addConstr(12.65 * patches_per_day + 0.78 * pen_testers <= 107, 
                    name="data_integrity_patches_pen_testers")
    model.addConstr(12.65 * patches_per_day + 0.78 * pen_testers + 14.19 * intrusion_analysts <= 131, 
                    name="data_integrity_all")

    # Non-negativity constraints
    model.addConstr(patches_per_day >= 0, name="patches_per_day_non_negative")
    model.addConstr(pen_testers >= 0, name="pen_testers_non_negative")
    model.addConstr(intrusion_analysts >= 0, name="intrusion_analysts_non_negative")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Patches per day: ", patches_per_day.varValue)
        print("Pen testers: ", pen_testers.varValue)
        print("Intrusion analysts: ", intrusion_analysts.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```