To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each of the objects mentioned (honeypots, system administrators, SOC operators), formulating the objective function using these variables, and then listing all constraints in terms of these variables.

Let's define:
- \(x_1\) as the number of honeypots,
- \(x_2\) as the number of system administrators,
- \(x_3\) as the number of SOC operators.

The objective function to maximize is: \(4.72x_1 + 8.14x_2 + 1.24x_3\).

The constraints based on the problem description are:
1. \(3.43x_1 + 3.96x_2 \geq 24\) (Total combined data integrity impact from honeypots and system administrators should be 24 or more.)
2. \(3.43x_1 + 3.96x_2 + 5.3x_3 \geq 19\) (Total combined data integrity impact from all three should be greater than or equal to 19.)
3. \(3.96x_2 + 5.3x_3 \leq 110\) (Total combined data integrity impact from system administrators and SOC operators must be 110 at maximum.)
4. \(3.43x_1 + 3.96x_2 + 5.3x_3 \leq 113\) (Total combined data integrity impact from all three has to be less than or equal to 113, as per the upper bound given for 'r0'.)
5. \(x_1, x_2, x_3 \in \mathbb{Z}^+\) (All variables must be positive integers, since you can't have a fraction of a honeypot, system administrator, or SOC operator.)

Thus, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'honeypots'), ('x2', 'system administrators'), ('x3', 'SOC operators')],
  'objective_function': '4.72*x1 + 8.14*x2 + 1.24*x3',
  'constraints': [
    '3.43*x1 + 3.96*x2 >= 24',
    '3.43*x1 + 3.96*x2 + 5.3*x3 >= 19',
    '3.96*x2 + 5.3*x3 <= 110',
    '3.43*x1 + 3.96*x2 + 5.3*x3 <= 113'
  ]
}
```

To solve this optimization problem using Gurobi, we can use the following Python code:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="honeypots")
x2 = m.addVar(vtype=GRB.INTEGER, name="system_administrators")
x3 = m.addVar(vtype=GRB.INTEGER, name="SOC_operators")

# Set objective function
m.setObjective(4.72*x1 + 8.14*x2 + 1.24*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3.43*x1 + 3.96*x2 >= 24, name="constraint_1")
m.addConstr(3.43*x1 + 3.96*x2 + 5.3*x3 >= 19, name="constraint_2")
m.addConstr(3.96*x2 + 5.3*x3 <= 110, name="constraint_3")
m.addConstr(3.43*x1 + 3.96*x2 + 5.3*x3 <= 113, name="constraint_4")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Honeypots: {x1.x}")
    print(f"System Administrators: {x2.x}")
    print(f"SOC Operators: {x3.x}")
else:
    print("No optimal solution found")
```