## Step 1: Define the symbolic representation of the variables
The variables are 'automatic alerts', 'security engineers', and 'network administrators', which we will denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $3x_1 + 4x_2 + 3x_3$.

## Step 3: Convert the constraints into a symbolic representation
The constraints are:
1. $15x_1 + x_2 + 19x_3 \leq 234$ (power consumption upper bound)
2. $x_2 + 19x_3 \geq 41$ (power consumption of security engineers and network administrators)
3. $15x_1 + x_2 \geq 53$ (power consumption of automatic alerts and security engineers)
4. $15x_1 + x_2 + 19x_3 \geq 40$ (minimum power consumption from all)
5. $15x_1 + x_2 + 19x_3 \geq 40$ (same as constraint 4, redundant)
6. $-2x_2 + 10x_3 \geq 0$ (relationship between security engineers and network administrators)
7. $x_1 \in \mathbb{Z}$ (automatic alerts are a nonfractional number)
8. $x_2 \in \mathbb{Z}$ (security engineers are a whole number)
9. $x_3 \in \mathbb{Z}$ (network administrators are a whole number)

## 4: Remove redundant constraints and prepare for Gurobi implementation
Removing the redundant constraint 5, we have:
- Objective function: $3x_1 + 4x_2 + 3x_3$
- Constraints:
  1. $15x_1 + x_2 + 19x_3 \leq 234$
  2. $x_2 + 19x_3 \geq 41$
  3. $15x_1 + x_2 \geq 53$
  4. $-2x_2 + 10x_3 \geq 0$
  And $x_1, x_2, x_3 \in \mathbb{Z}$.

## 5: Implement the problem in Gurobi
```python
import gurobi

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

# Define the variables
x1 = model.addVar(name="automatic_alerts", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="security_engineers", vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name="network_administrators", vtype=gurobi.GRB.INTEGER)

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

# Constraints
model.addConstr(15*x1 + x2 + 19*x3 <= 234, name="power_consumption_upper_bound")
model.addConstr(x2 + 19*x3 >= 41, name="security_engineers_network_administrators_power")
model.addConstr(15*x1 + x2 >= 53, name="automatic_alerts_security_engineers_power")
model.addConstr(-2*x2 + 10*x3 >= 0, name="security_engineers_network_administrators_relationship")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Automatic Alerts: ", x1.varValue)
    print("Security Engineers: ", x2.varValue)
    print("Network Administrators: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 6: Provide the symbolic representation
```json
{
    'sym_variables': [('x1', 'automatic alerts'), ('x2', 'security engineers'), ('x3', 'network administrators')],
    'objective_function': '3*x1 + 4*x2 + 3*x3',
    'constraints': [
        '15*x1 + x2 + 19*x3 <= 234',
        'x2 + 19*x3 >= 41',
        '15*x1 + x2 >= 53',
        '-2*x2 + 10*x3 >= 0'
    ]
}
```