## Problem Description and Symbolic Representation

The problem requires finding the optimal number of computer engineers and software engineers to minimize labor costs while satisfying certain constraints.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$ : Number of computer engineers
- $x_2$ : Number of software engineers

The objective is to minimize the total labor cost:
- Objective function: $1000x_1 + 800x_2$

The constraints are:
1. Total engineers: $x_1 + x_2 \geq 50$
2. Minimum computer engineers: $x_1 \geq 10$
3. Software engineers vs. computer engineers: $x_2 \geq 2x_1$
4. Non-negativity: $x_1 \geq 0, x_2 \geq 0$

However, since $x_1$ and $x_2$ represent the number of engineers, we implicitly assume $x_1 \geq 0, x_2 \geq 0$. The explicit non-negativity constraints for $x_1$ and $x_2$ are thus redundant given the context but will be considered for completeness.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'computer engineers'), ('x2', 'software engineers')],
    'objective_function': '1000*x1 + 800*x2',
    'constraints': [
        'x1 + x2 >= 50',
        'x1 >= 10',
        'x2 >= 2*x1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_engineer_hiring_problem():
    # Create a new model
    model = gp.Model("engineer_hiring")

    # Define variables
    x1 = model.addVar(name="computer_engineers", lb=0, vtype=gp.GRB.INTEGER)
    x2 = model.addVar(name="software_engineers", lb=0, vtype=gp.GRB.INTEGER)

    # Objective function: Minimize labor cost
    model.setObjective(1000*x1 + 800*x2, gp.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x1 + x2 >= 50, name="total_engineers")
    model.addConstr(x1 >= 10, name="min_computer_engineers")
    model.addConstr(x2 >= 2*x1, name="software_vs_computer")

    # Solve the model
    model.optimize()

    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution found.")
        print(f"Number of computer engineers: {x1.varValue}")
        print(f"Number of software engineers: {x2.varValue}")
        print(f"Minimum labor cost: ${model.objVal}")
    elif model.status == gp.GRB.INFEASIBLE:
        print("No feasible solution exists.")
    else:
        print("Optimization failed.")

solve_engineer_hiring_problem()
```