## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Laura', 'hours worked by Bobby', 'hours worked by Dale', 'hours worked by George'] which can be represented symbolically as 'x1', 'x2', 'x3', 'x4' respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- 'x1' for 'hours worked by Laura'
- 'x2' for 'hours worked by Bobby'
- 'x3' for 'hours worked by Dale'
- 'x4' for 'hours worked by George'

## 3: Define the objective function in symbolic notation
The objective function to minimize is: $4x_1 + 3x_2 + 7x_3 + 5x_4$

## 4: List the constraints in symbolic notation
The constraints are:
1. $2x_2 + 3x_4 \geq 9$
2. $5x_3 + 3x_4 \geq 13$
3. $6x_1 + 2x_2 + 5x_3 + 3x_4 \geq 13$
4. $10x_3 - 2x_4 \geq 0$
5. $4x_1 - x_3 \geq 0$
6. $6x_1 + 2x_2 + 5x_3 \leq 44$
7. $x_1, x_2, x_3, x_4$ are integers.

## 5: Create the symbolic representation dictionary
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by Bobby'), ('x3', 'hours worked by Dale'), ('x4', 'hours worked by George')],
    'objective_function': '4*x1 + 3*x2 + 7*x3 + 5*x4',
    'constraints': [
        '2*x2 + 3*x4 >= 9',
        '5*x3 + 3*x4 >= 13',
        '6*x1 + 2*x2 + 5*x3 + 3*x4 >= 13',
        '10*x3 - 2*x4 >= 0',
        '4*x1 - x3 >= 0',
        '6*x1 + 2*x2 + 5*x3 <= 44',
        'x1, x2, x3, x4 are integers'
    ]
}
```

## 6: Write the Gurobi code
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='hours_worked_by_Laura', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='hours_worked_by_Bobby', vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name='hours_worked_by_Dale', vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name='hours_worked_by_George', vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(4*x1 + 3*x2 + 7*x3 + 5*x4, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(2*x2 + 3*x4 >= 9)
    model.addConstr(5*x3 + 3*x4 >= 13)
    model.addConstr(6*x1 + 2*x2 + 5*x3 + 3*x4 >= 13)
    model.addConstr(10*x3 - 2*x4 >= 0)
    model.addConstr(4*x1 - x3 >= 0)
    model.addConstr(6*x1 + 2*x2 + 5*x3 <= 44)

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Hours worked by Laura: ', x1.varValue)
        print('Hours worked by Bobby: ', x2.varValue)
        print('Hours worked by Dale: ', x3.varValue)
        print('Hours worked by George: ', x4.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```