## Problem Description and Formulation

The problem is an optimization problem where we need to maximize an objective function subject to several constraints. The objective function is to maximize \(4.72 \times \text{honeypots} + 8.14 \times \text{system administrators} + 1.24 \times \text{SOC operators}\).

The constraints are as follows:
- The data integrity impact of honeypots is \(3.43 \times \text{honeypots}\).
- The data integrity impact of system administrators is \(3.96 \times \text{system administrators}\).
- The data integrity impact of SOC operators is \(5.3 \times \text{SOC operators}\).
- The total data integrity impact from honeypots and system administrators should be 24 or more: \(3.43 \times \text{honeypots} + 3.96 \times \text{system administrators} \geq 24\).
- The total data integrity impact from all three should be greater than or equal to 19: \(3.43 \times \text{honeypots} + 3.96 \times \text{system administrators} + 5.3 \times \text{SOC operators} \geq 19\).
- The total data integrity impact from system administrators and SOC operators should be at most 110: \(3.96 \times \text{system administrators} + 5.3 \times \text{SOC operators} \leq 110\).
- The total data integrity impact from all three should be at most 110: \(3.43 \times \text{honeypots} + 3.96 \times \text{system administrators} + 5.3 \times \text{SOC operators} \leq 110\).
- The number of honeypots, system administrators, and SOC operators must be whole numbers.

## Gurobi Code Formulation

```python
import gurobipy as gp

# Define the model
model = gp.Model("optimization_problem")

# Define the variables
honeypots = model.addVar(name="honeypots", vtype=gp.GRB.INTEGER)
system_administrators = model.addVar(name="system_administrators", vtype=gp.GRB.INTEGER)
SOC_operators = model.addVar(name="SOC_operators", vtype=gp.GRB.INTEGER)

# Objective function
model.setObjective(4.72 * honeypots + 8.14 * system_administrators + 1.24 * SOC_operators, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(3.43 * honeypots + 3.96 * system_administrators >= 24, name="constraint_1")
model.addConstr(3.43 * honeypots + 3.96 * system_administrators + 5.3 * SOC_operators >= 19, name="constraint_2")
model.addConstr(3.96 * system_administrators + 5.3 * SOC_operators <= 110, name="constraint_3")
model.addConstr(3.43 * honeypots + 3.96 * system_administrators + 5.3 * SOC_operators <= 110, name="constraint_4")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Honeypots: ", honeypots.varValue)
    print("System Administrators: ", system_administrators.varValue)
    print("SOC Operators: ", SOC_operators.varValue)
else:
    print("The model is infeasible")
```