## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by George', 'hours worked by Peggy', and 'hours worked by Mary', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : hours worked by George
- $x_1$ : hours worked by Peggy
- $x_2$ : hours worked by Mary

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is $1.57x_0 + 7.49x_1 + 9.9x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $4x_0 + 11x_1 + 5x_2 \leq 136$ (organization score)
- $6x_0 + x_1 + 4x_2 \leq 235$ (work quality rating)
- $11x_0 + 8x_1 + 14x_2 \leq 123$ (productivity rating)
- $3x_0 + x_1 + 6x_2 \leq 135$ (computer competence rating)
- $4x_0 + 11x_1 \geq 15$ (combined organization score)
- $6x_0 + x_1 \geq 51$ (combined work quality rating)
- $11x_0 + 8x_1 \geq 13$ (combined productivity rating)
- $11x_0 + 14x_2 \geq 20$ (combined productivity rating)
- $3x_0 + 6x_2 \geq 38$ (combined computer competence rating)
- $11x_1 + 5x_2 \leq 129$ (combined organization score)
- $4x_0 + 11x_1 \leq 49$ (combined organization score)
- $4x_0 + 11x_1 + 5x_2 \leq 49$ (combined organization score)
- $6x_0 + 4x_2 \leq 189$ (combined work quality rating)
- $6x_0 + x_1 \leq 165$ (combined work quality rating)
- $6x_0 + x_1 + 4x_2 \leq 212$ (combined work quality rating)
- $11x_0 + 14x_2 \leq 100$ (combined productivity rating)
- $11x_0 + 8x_1 \leq 62$ (combined productivity rating)
- $8x_1 + 14x_2 \leq 79$ (combined productivity rating)
- $11x_0 + 8x_1 + 14x_2 \leq 79$ (combined productivity rating)
- $x_1 + 6x_2 \leq 117$ (combined computer competence rating)
- $3x_0 + 6x_2 \leq 45$ (combined computer competence rating)
- $3x_0 + x_1 + 6x_2 \leq 45$ (combined computer competence rating)

## 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by George'), ('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Mary')],
    'objective_function': '1.57*x0 + 7.49*x1 + 9.9*x2',
    'constraints': [
        '4*x0 + 11*x1 + 5*x2 <= 136',
        '6*x0 + x1 + 4*x2 <= 235',
        '11*x0 + 8*x1 + 14*x2 <= 123',
        '3*x0 + x1 + 6*x2 <= 135',
        '4*x0 + 11*x1 >= 15',
        '6*x0 + x1 >= 51',
        '11*x0 + 8*x1 >= 13',
        '11*x0 + 14*x2 >= 20',
        '3*x0 + 6*x2 >= 38',
        '11*x1 + 5*x2 <= 129',
        '4*x0 + 11*x1 <= 49',
        '4*x0 + 11*x1 + 5*x2 <= 49',
        '6*x0 + 4*x2 <= 189',
        '6*x0 + x1 <= 165',
        '6*x0 + x1 + 4*x2 <= 212',
        '11*x0 + 14*x2 <= 100',
        '11*x0 + 8*x1 <= 62',
        '8*x1 + 14*x2 <= 79',
        '11*x0 + 8*x1 + 14*x2 <= 79',
        'x1 + 6*x2 <= 117',
        '3*x0 + 6*x2 <= 45',
        '3*x0 + x1 + 6*x2 <= 45'
    ]
}
```

## 6: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by George
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Peggy
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Mary

    # Define the objective function
    model.setObjective(1.57 * x0 + 7.49 * x1 + 9.9 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(4 * x0 + 11 * x1 + 5 * x2 <= 136)
    model.addConstr(6 * x0 + x1 + 4 * x2 <= 235)
    model.addConstr(11 * x0 + 8 * x1 + 14 * x2 <= 123)
    model.addConstr(3 * x0 + x1 + 6 * x2 <= 135)
    model.addConstr(4 * x0 + 11 * x1 >= 15)
    model.addConstr(6 * x0 + x1 >= 51)
    model.addConstr(11 * x0 + 8 * x1 >= 13)
    model.addConstr(11 * x0 + 14 * x2 >= 20)
    model.addConstr(3 * x0 + 6 * x2 >= 38)
    model.addConstr(11 * x1 + 5 * x2 <= 129)
    model.addConstr(4 * x0 + 11 * x1 <= 49)
    model.addConstr(4 * x0 + 11 * x1 + 5 * x2 <= 49)
    model.addConstr(6 * x0 + 4 * x2 <= 189)
    model.addConstr(6 * x0 + x1 <= 165)
    model.addConstr(6 * x0 + x1 + 4 * x2 <= 212)
    model.addConstr(11 * x0 + 14 * x2 <= 100)
    model.addConstr(11 * x0 + 8 * x1 <= 62)
    model.addConstr(8 * x1 + 14 * x2 <= 79)
    model.addConstr(11 * x0 + 8 * x1 + 14 * x2 <= 79)
    model.addConstr(x1 + 6 * x2 <= 117)
    model.addConstr(3 * x0 + 6 * x2 <= 45)
    model.addConstr(3 * x0 + x1 + 6 * x2 <= 45)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by George: ", x0.varValue)
        print("Hours worked by Peggy: ", x1.varValue)
        print("Hours worked by Mary: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```