To tackle this optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each of the elements mentioned (automatic alerts, security engineers, network administrators), formulating the objective function using these variables, and then expressing the constraints in terms of these variables as well.

Let's denote:
- \(x_1\) as the number of automatic alerts,
- \(x_2\) as the number of security engineers,
- \(x_3\) as the number of network administrators.

The objective function is to minimize: \(3x_1 + 4x_2 + 3x_3\).

Given constraints:
1. Power consumption from each source must not exceed given bounds, but specific upper bounds for each are not provided except for their contributions.
2. The power consumption of security engineers plus network administrators must be at least 41 kWh: \(x_2 + 19x_3 \geq 41\).
3. Automatic alerts and security engineers must contribute at least 53 kWh: \(15x_1 + x_2 \geq 53\).
4. The minimum power consumption from all sources must be 40 kWh: \(15x_1 + x_2 + 19x_3 \geq 40\).
5. Another constraint on the total minimum power consumption is mentioned but seems redundant given the previous one.
6. A constraint involving security engineers and network administrators: \(-2x_2 + 10x_3 \geq 0\).

All variables must be non-negative integers (whole numbers).

Here's a symbolic representation of the problem:
```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 >= 40',
    'x2 + 19*x3 >= 41',
    '15*x1 + x2 >= 53',
    '-2*x2 + 10*x3 >= 0'
  ]
}
```

Now, let's write the Gurobi code for this problem:
```python
from gurobipy import *

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

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

# Set objective function
m.setObjective(3*x1 + 4*x2 + 3*x3, GRB.MINIMIZE)

# Add constraints
m.addConstr(15*x1 + x2 + 19*x3 >= 40, "total_power_consumption")
m.addConstr(x2 + 19*x3 >= 41, "security_and_network_power")
m.addConstr(15*x1 + x2 >= 53, "alerts_and_security_power")
m.addConstr(-2*x2 + 10*x3 >= 0, "security_vs_network")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Automatic Alerts: {x1.x}")
    print(f"Security Engineers: {x2.x}")
    print(f"Network Administrators: {x3.x}")
else:
    print("No optimal solution found")
```