## Problem Description and Symbolic Representation

The problem involves a gardening company that needs to employ newcomers and full-time employees to meet certain requirements while minimizing the wage bill.

### Symbolic Variables:
- $x_1$: Number of newcomers
- $x_2$: Number of full-time employees

### Objective Function:
The objective is to minimize the total wage bill, which can be represented as $400x_1 + 700x_2$.

### Constraints:
1. The company needs at least 100 gardeners: $x_1 + x_2 \geq 100$
2. At least 40 must be full-time employees: $x_2 \geq 40$
3. The number of full-time employees should be at least half the number of newcomers: $x_2 \geq 0.5x_1$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'newcomers'), ('x2', 'full-time employees')],
    'objective_function': '400*x1 + 700*x2',
    'constraints': [
        'x1 + x2 >= 100',
        'x2 >= 40',
        'x2 >= 0.5*x1'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

def solve_gardening_company_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name='newcomers', lb=0, vtype=gurobi.GRB.INTEGER)  # Number of newcomers
    x2 = model.addVar(name='full_time_employees', lb=0, vtype=gurobi.GRB.INTEGER)  # Number of full-time employees

    # Objective function: Minimize the wage bill
    model.setObjective(400 * x1 + 700 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x1 + x2 >= 100, name='total_gardeners')  # At least 100 gardeners
    model.addConstr(x2 >= 40, name='min_full_time')  # At least 40 full-time employees
    model.addConstr(x2 >= 0.5 * x1, name='supervision_requirement')  # Full-time employees >= half of newcomers

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution:")
        print(f"Newcomers: {x1.varValue}")
        print(f"Full-time employees: {x2.varValue}")
        print(f"Minimum wage bill: ${400*x1.varValue + 700*x2.varValue}")
    else:
        print("The problem is infeasible.")

solve_gardening_company_problem()
```