To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints in terms of these variables.

Let's denote:
- $x_1$ as the number of computer engineers,
- $x_2$ as the number of software engineers.

The objective is to minimize the labor cost, which can be represented by the objective function: $1000x_1 + 800x_2$.

The constraints given are:
1. The total number of engineers should be at least 50: $x_1 + x_2 \geq 50$.
2. At least 10 computer engineers must be hired: $x_1 \geq 10$.
3. The number of software engineers should be at least twice the number of computer engineers: $x_2 \geq 2x_1$.

All variables ($x_1$, $x_2$) represent non-negative integers since we cannot hire a fraction of an engineer.

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of computer engineers'), ('x2', 'number of software engineers')],
    'objective_function': '1000*x1 + 800*x2',
    'constraints': ['x1 + x2 >= 50', 'x1 >= 10', 'x2 >= 2*x1']
}
```

To solve this optimization problem using Gurobi in Python, we can write the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="computer_engineers")
x2 = m.addVar(vtype=GRB.INTEGER, name="software_engineers")

# Set objective function
m.setObjective(1000*x1 + 800*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(x1 + x2 >= 50, "total_engineers")
m.addConstr(x1 >= 10, "min_computer_engineers")
m.addConstr(x2 >= 2*x1, "software_to_computer_ratio")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Computer Engineers: {x1.x}")
    print(f"Software Engineers: {x2.x}")
    print(f"Total Cost: ${1000*x1.x + 800*x2.x}")
else:
    print("No optimal solution found")
```