## Step 1: Define the symbolic representation of the variables
The variables are 'honeypots', 'system administrators', and 'SOC operators', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_1$ for 'honeypots'
- $x_2$ for 'system administrators'
- $x_3$ for 'SOC operators'

## 3: Define the objective function in symbolic notation
The objective function to maximize is $4.72x_1 + 8.14x_2 + 1.24x_3$.

## 4: Define the constraints in symbolic notation
The constraints are:
- $3.43x_1 \leq 113$
- $3.96x_2 \leq 113$
- $5.3x_3 \leq 113$
- $3.43x_1 + 3.96x_2 \geq 24$
- $3.43x_1 + 3.96x_2 + 5.3x_3 \geq 19$
- $3.96x_2 + 5.3x_3 \leq 110$
- $3.43x_1 + 3.96x_2 + 5.3x_3 \leq 110$
- $x_1, x_2, x_3$ are integers

## 5: Express the problem in the required JSON format
```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 <= 113',
        '3.96*x2 <= 113',
        '5.3*x3 <= 113',
        '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 <= 110',
        'x1, x2, x3 are integers'
    ]
}
```

## Step 6: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

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

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

# Define the constraints
m.addConstr(3.43*x1 <= 113)
m.addConstr(3.96*x2 <= 113)
m.addConstr(5.3*x3 <= 113)
m.addConstr(3.43*x1 + 3.96*x2 >= 24)
m.addConstr(3.43*x1 + 3.96*x2 + 5.3*x3 >= 19)
m.addConstr(3.96*x2 + 5.3*x3 <= 110)
m.addConstr(3.43*x1 + 3.96*x2 + 5.3*x3 <= 110)

# Optimize the model
m.optimize()

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