## Step 1: Define the symbolic representation of the variables
The variables are ['security engineers', 'system administrators', 'network administrators', 'pen testers'] which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The objective function to minimize is $2x_0 + 1x_1 + 7x_2 + 6x_3$.

## Step 3: List all the constraints in symbolic notation
Constraints:
1. $x_0 \geq 0$ and is an integer,
2. $x_1 \geq 0$ and is an integer,
3. $x_2 \geq 0$ and is an integer,
4. $x_3 \geq 0$ and is an integer,
5. $x_0 + 11x_1 \geq 13$,
6. $x_0 + 7x_3 \geq 15$,
7. $5x_2 + 7x_3 \geq 15$,
8. $x_0 + 11x_1 + 5x_2 + 7x_3 \geq 15$,
9. $x_2 + 7x_3 \geq 15$,
10. $x_1 + x_2 \geq 20$,
11. $9x_0 + x_2 \geq 16$,
12. $9x_0 + x_2 + 7x_3 \geq 22$,
13. $9x_0 + 4x_1 + x_2 + 7x_3 \geq 22$,
14. $14x_0 + 12x_1 \geq 13$,
15. $14x_0 + 4x_2 \geq 11$,
16. $12x_1 + 4x_3 \geq 11$,
17. $14x_0 + 4x_3 \geq 21$,
18. $14x_0 + 12x_1 + 4x_3 \geq 18$,
19. $12x_1 + 4x_2 + 4x_3 \geq 18$,
20. $14x_0 + 12x_1 + 4x_3 \geq 18$,
21. $12x_1 + 4x_2 + 4x_3 \geq 18$,
22. $14x_0 + 12x_1 + 4x_2 + 4x_3 \geq 18$,
23. $10x_1 - 7x_3 \geq 0$,
24. $5x_2 - 6x_3 \geq 0$,
25. $5x_2 + 7x_3 \leq 104$,
26. $x_0 + 7x_3 \leq 54$,
27. $x_0 + 11x_1 + 5x_2 \leq 49$,
28. $11x_1 + 5x_2 + 7x_3 \leq 75$,
29. $9x_0 + 7x_3 \leq 34$,
30. $9x_0 + 4x_1 + 7x_3 \leq 36$,
31. $12x_1 + 4x_3 \leq 74$,
32. $12x_1 + 4x_2 \leq 70$.

## Step 4: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables.

## 5: Implement the objective function and constraints in Gurobi

```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="security_engineers", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="system_administrators", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="network_administrators", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="pen_testers", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(2*x0 + x1 + 7*x2 + 6*x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(x0 + 11*x1 >= 13)
m.addConstr(x0 + 7*x3 >= 15)
m.addConstr(5*x2 + 7*x3 >= 15)
m.addConstr(x0 + 11*x1 + 5*x2 + 7*x3 >= 15)
m.addConstr(x2 + 7*x3 >= 15)
m.addConstr(x1 + x2 >= 20)
m.addConstr(9*x0 + x2 >= 16)
m.addConstr(9*x0 + x2 + 7*x3 >= 22)
m.addConstr(9*x0 + 4*x1 + x2 + 7*x3 >= 22)
m.addConstr(14*x0 + 12*x1 >= 13)
m.addConstr(14*x0 + 4*x2 >= 11)
m.addConstr(12*x1 + 4*x3 >= 11)
m.addConstr(14*x0 + 4*x3 >= 21)
m.addConstr(14*x0 + 12*x1 + 4*x3 >= 18)
m.addConstr(12*x1 + 4*x2 + 4*x3 >= 18)
m.addConstr(14*x0 + 12*x1 + 4*x3 >= 18)
m.addConstr(12*x1 + 4*x2 + 4*x3 >= 18)
m.addConstr(14*x0 + 12*x1 + 4*x2 + 4*x3 >= 18)
m.addConstr(10*x1 - 7*x3 >= 0)
m.addConstr(5*x2 - 6*x3 >= 0)
m.addConstr(5*x2 + 7*x3 <= 104)
m.addConstr(x0 + 7*x3 <= 54)
m.addConstr(x0 + 11*x1 + 5*x2 <= 49)
m.addConstr(11*x1 + 5*x2 + 7*x3 <= 75)
m.addConstr(9*x0 + 7*x3 <= 34)
m.addConstr(9*x0 + 4*x1 + 7*x3 <= 36)
m.addConstr(12*x1 + 4*x3 <= 74)
m.addConstr(12*x1 + 4*x2 <= 70)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Security Engineers: ", x0.varValue)
    print("System Administrators: ", x1.varValue)
    print("Network Administrators: ", x2.varValue)
    print("Pen Testers: ", x3.varValue)
else:
    print("The model is infeasible")
```

```json
{
    'sym_variables': [
        ('x0', 'security engineers'),
        ('x1', 'system administrators'),
        ('x2', 'network administrators'),
        ('x3', 'pen testers')
    ],
    'objective_function': '2*x0 + x1 + 7*x2 + 6*x3',
    'constraints': [
        'x0 + 11*x1 >= 13',
        'x0 + 7*x3 >= 15',
        '5*x2 + 7*x3 >= 15',
        'x0 + 11*x1 + 5*x2 + 7*x3 >= 15',
        'x2 + 7*x3 >= 15',
        'x1 + x2 >= 20',
        '9*x0 + x2 >= 16',
        '9*x0 + x2 + 7*x3 >= 22',
        '9*x0 + 4*x1 + x2 + 7*x3 >= 22',
        '14*x0 + 12*x1 >= 13',
        '14*x0 + 4*x2 >= 11',
        '12*x1 + 4*x3 >= 11',
        '14*x0 + 4*x3 >= 21',
        '14*x0 + 12*x1 + 4*x3 >= 18',
        '12*x1 + 4*x2 + 4*x3 >= 18',
        '14*x0 + 12*x1 + 4*x3 >= 18',
        '12*x1 + 4*x2 + 4*x3 >= 18',
        '14*x0 + 12*x1 + 4*x2 + 4*x3 >= 18',
        '10*x1 - 7*x3 >= 0',
        '5*x2 - 6*x3 >= 0',
        '5*x2 + 7*x3 <= 104',
        'x0 + 7*x3 <= 54',
        'x0 + 11*x1 + 5*x2 <= 49',
        '11*x1 + 5*x2 + 7*x3 <= 75',
        '9*x0 + 7*x3 <= 34',
        '9*x0 + 4*x1 + 7*x3 <= 36',
        '12*x1 + 4*x3 <= 74',
        '12*x1 + 4*x2 <= 70'
    ]
}
```