## Step 1: Define the symbolic representation of the variables
The variables are: 
- 'pen testers' 
- 'system administrators' 
- 'automatic alerts' 
- 'network administrators'

Let's denote them as:
- $x_0$ : pen testers
- $x_1$ : system administrators
- $x_2$ : automatic alerts
- $x_3$ : network administrators

## Step 2: Formulate the objective function
The objective function to minimize is: $9x_0 + 4x_1 + 3x_2 + 7x_3$

## Step 3: Define the constraints
### Resource constraints
- Network latency impact: $27x_0 + 21x_1 + 31x_2 + 28x_3$
- Dollar cost: $5x_0 + 17x_1 + 29x_2 + 31x_3$
- Network integrity impact: $24x_0 + 22x_1 + 11x_2 + 7x_3$
- Data accessibility impact: $21x_0 + 31x_1 + 31x_2 + 12x_3$

### Given constraints
- $21x_1 + 28x_3 \geq 34$
- $27x_0 + 31x_2 \geq 43$
- $27x_0 + 21x_1 + 31x_2 + 28x_3 \geq 43$
- $5x_0 + 17x_1 \geq 160$
- $29x_2 + 31x_3 \geq 70$
- $17x_1 + 31x_3 \geq 165$
- $5x_0 + 29x_2 \geq 80$
- $17x_1 + 29x_2 + 31x_3 \geq 178$
- $5x_0 + 17x_1 + 29x_2 + 31x_3 \geq 178$
- $24x_0 + 11x_2 \geq 107$
- $24x_0 + 7x_3 \geq 75$
- $22x_1 + 11x_2 \geq 124$
- $24x_0 + 22x_1 \geq 87$
- $11x_2 + 7x_3 \geq 60$
- $24x_0 + 22x_1 + 11x_2 + 7x_3 \geq 60$
- $21x_0 + 31x_1 \geq 123$
- $21x_0 + 31x_2 \geq 77$
- $31x_1 + 31x_2 \geq 126$
- $31x_2 + 12x_3 \geq 96$
- $21x_0 + 12x_3 \geq 74$
- $21x_0 + 31x_1 + 31x_2 + 12x_3 \geq 74$
- $4x_0 - 7x_1 \geq 0$
- $-x_0 + 4x_3 \geq 0$
- $17x_1 + 29x_2 \leq 681$
- $5x_0 + 29x_2 \leq 346$
- $5x_0 + 17x_1 \leq 316$
- $29x_2 + 31x_3 \leq 309$
- $5x_0 + 17x_1 + 31x_3 \leq 775$
- $11x_2 + 7x_3 \leq 411$
- $31x_2 + 12x_3 \leq 277$
- $31x_1 + 12x_3 \leq 166$
- $31x_1 + 31x_2 \leq 525$
- $21x_0 + 31x_1 \leq 166$
- $21x_0 + 31x_2 \leq 484$
- $31x_1 + 31x_2 + 12x_3 \leq 439$
- $21x_0 + 31x_1 + 12x_3 \leq 317$

## 4: Symbolic representation
```json
{
    'sym_variables': [
        ('x0', 'pen testers'),
        ('x1', 'system administrators'),
        ('x2', 'automatic alerts'),
        ('x3', 'network administrators')
    ],
    'objective_function': '9*x0 + 4*x1 + 3*x2 + 7*x3',
    'constraints': [
        '27*x0 + 21*x1 + 31*x2 + 28*x3 <= 229',
        '5*x0 + 17*x1 + 29*x2 + 31*x3 <= 781',
        '24*x0 + 22*x1 + 11*x2 + 7*x3 <= 497',
        '21*x0 + 31*x1 + 31*x2 + 12*x3 <= 580',
        '21*x1 + 28*x3 >= 34',
        '27*x0 + 31*x2 >= 43',
        '27*x0 + 21*x1 + 31*x2 + 28*x3 >= 43',
        '5*x0 + 17*x1 >= 160',
        '29*x2 + 31*x3 >= 70',
        '17*x1 + 31*x3 >= 165',
        '5*x0 + 29*x2 >= 80',
        '17*x1 + 29*x2 + 31*x3 >= 178',
        '5*x0 + 17*x1 + 29*x2 + 31*x3 >= 178',
        '24*x0 + 11*x2 >= 107',
        '24*x0 + 7*x3 >= 75',
        '22*x1 + 11*x2 >= 124',
        '24*x0 + 22*x1 >= 87',
        '11*x2 + 7*x3 >= 60',
        '24*x0 + 22*x1 + 11*x2 + 7*x3 >= 60',
        '21*x0 + 31*x1 >= 123',
        '21*x0 + 31*x2 >= 77',
        '31*x1 + 31*x2 >= 126',
        '31*x2 + 12*x3 >= 96',
        '21*x0 + 12*x3 >= 74',
        '21*x0 + 31*x1 + 31*x2 + 12*x3 >= 74',
        '4*x0 - 7*x1 >= 0',
        '-x0 + 4*x3 >= 0',
        '17*x1 + 29*x2 <= 681',
        '5*x0 + 29*x2 <= 346',
        '5*x0 + 17*x1 <= 316',
        '29*x2 + 31*x3 <= 309',
        '5*x0 + 17*x1 + 31*x3 <= 775',
        '11*x2 + 7*x3 <= 411',
        '31*x2 + 12*x3 <= 277',
        '31*x1 + 12*x3 <= 166',
        '31*x1 + 31*x2 <= 525',
        '21*x0 + 31*x1 <= 166',
        '21*x0 + 31*x2 <= 484',
        '31*x1 + 31*x2 + 12*x3 <= 439',
        '21*x0 + 31*x1 + 12*x3 <= 317',
        'x0 % 1 == 0',
        'x1 % 1 == 0',
        'x2 % 1 == 0',
        'x3 % 1 == 0'
    ]
}
```

## 5: Gurobi code
```python
import gurobi

def optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name='x0', vtype=gurobi.GRB.INTEGER)  # pen testers
    x1 = model.addVar(name='x1', vtype=gurobi.GRB.INTEGER)  # system administrators
    x2 = model.addVar(name='x2', vtype=gurobi.GRB.INTEGER)  # automatic alerts
    x3 = model.addVar(name='x3', vtype=gurobi.GRB.INTEGER)  # network administrators

    # Objective function
    model.setObjective(9 * x0 + 4 * x1 + 3 * x2 + 7 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(27 * x0 + 21 * x1 + 31 * x2 + 28 * x3 <= 229)
    model.addConstr(5 * x0 + 17 * x1 + 29 * x2 + 31 * x3 <= 781)
    model.addConstr(24 * x0 + 22 * x1 + 11 * x2 + 7 * x3 <= 497)
    model.addConstr(21 * x0 + 31 * x1 + 31 * x2 + 12 * x3 <= 580)
    model.addConstr(21 * x1 + 28 * x3 >= 34)
    model.addConstr(27 * x0 + 31 * x2 >= 43)
    model.addConstr(27 * x0 + 21 * x1 + 31 * x2 + 28 * x3 >= 43)
    model.addConstr(5 * x0 + 17 * x1 >= 160)
    model.addConstr(29 * x2 + 31 * x3 >= 70)
    model.addConstr(17 * x1 + 31 * x3 >= 165)
    model.addConstr(5 * x0 + 29 * x2 >= 80)
    model.addConstr(17 * x1 + 29 * x2 + 31 * x3 >= 178)
    model.addConstr(5 * x0 + 17 * x1 + 29 * x2 + 31 * x3 >= 178)
    model.addConstr(24 * x0 + 11 * x2 >= 107)
    model.addConstr(24 * x0 + 7 * x3 >= 75)
    model.addConstr(22 * x1 + 11 * x2 >= 124)
    model.addConstr(24 * x0 + 22 * x1 >= 87)
    model.addConstr(11 * x2 + 7 * x3 >= 60)
    model.addConstr(24 * x0 + 22 * x1 + 11 * x2 + 7 * x3 >= 60)
    model.addConstr(21 * x0 + 31 * x1 >= 123)
    model.addConstr(21 * x0 + 31 * x2 >= 77)
    model.addConstr(31 * x1 + 31 * x2 >= 126)
    model.addConstr(31 * x2 + 12 * x3 >= 96)
    model.addConstr(21 * x0 + 12 * x3 >= 74)
    model.addConstr(21 * x0 + 31 * x1 + 31 * x2 + 12 * x3 >= 74)
    model.addConstr(4 * x0 - 7 * x1 >= 0)
    model.addConstr(-x0 + 4 * x3 >= 0)
    model.addConstr(17 * x1 + 29 * x2 <= 681)
    model.addConstr(5 * x0 + 29 * x2 <= 346)
    model.addConstr(5 * x0 + 17 * x1 <= 316)
    model.addConstr(29 * x2 + 31 * x3 <= 309)
    model.addConstr(5 * x0 + 17 * x1 + 31 * x3 <= 775)
    model.addConstr(11 * x2 + 7 * x3 <= 411)
    model.addConstr(31 * x2 + 12 * x3 <= 277)
    model.addConstr(31 * x1 + 12 * x3 <= 166)
    model.addConstr(31 * x1 + 31 * x2 <= 525)
    model.addConstr(21 * x0 + 31 * x1 <= 166)
    model.addConstr(21 * x0 + 31 * x2 <= 484)
    model.addConstr(31 * x1 + 31 * x2 + 12 * x3 <= 439)
    model.addConstr(21 * x0 + 31 * x1 + 12 * x3 <= 317)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('x0: ', x0.varValue)
        print('x1: ', x1.varValue)
        print('x2: ', x2.varValue)
        print('x3: ', x3.varValue)
    else:
        print('No optimal solution found')

optimization_problem()
```