## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The objective function to minimize is \(4x_0^2 + 4x_0\), where \(x_0\) represents the Mbps bandwidth allocated to monitoring. The variables are \(x_0\) (Mbps bandwidth allocated to monitoring) and \(x_1\) (number of network administrators).

## Resources/Attributes

- \(r_0\): dollar cost, with \(x_0\) costing $17 and \(x_1\) costing $9. The total cost must be between $15 and $57.
- \(r_1\): data integrity impact, with \(x_0\) having an impact of 17 and \(x_1\) having an impact of 17. The total impact must be at least 11 and the combined squared impact must not exceed 18.

## Constraints

1. **Cost Constraints**: The total cost is \(17x_0 + 9x_1 \geq 15\) and \(17x_0 + 9x_1 \leq 57\).
2. **Data Integrity Impact**: \(17x_0 + 17x_1 \geq 11\).
3. **Combined Impact Squared**: \(17^2x_0^2 + 17^2x_1^2 \leq 18\).
4. **Linear Constraint**: \(4x_0 - 6x_1 \geq 0\).
5. **Variable Constraints**: \(x_0\) must be an integer and \(x_1\) must be an integer.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="Mbps_bandwidth_allocated_to_monitoring", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="network_administrators", vtype=gurobi.GRB.INTEGER)

    # Objective function: Minimize 4*x0^2 + 4*x0
    model.setObjective(4*x0**2 + 4*x0, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(17*x0 + 9*x1 >= 15, name="cost_constraint_min")
    model.addConstr(17*x0 + 9*x1 <= 57, name="cost_constraint_max")
    model.addConstr(17*x0 + 17*x1 >= 11, name="data_integrity_impact")
    model.addConstr(17**2*x0**2 + 17**2*x1**2 <= 18, name="combined_impact_squared")
    model.addConstr(4*x0 - 6*x1 >= 0, name="linear_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Mbps bandwidth allocated to monitoring: {x0.varValue}")
        print(f"Network administrators: {x1.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```

This code defines the optimization problem using Gurobi, with the specified objective function and constraints. It then solves the problem and prints out the optimal solution if one is found.