## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Paul', 'hours worked by Hank', 'hours worked by Mary'], which can be represented symbolically as 'x1', 'x2', and 'x3' respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- 'x1' for 'hours worked by Paul'
- 'x2' for 'hours worked by Hank'
- 'x3' for 'hours worked by Mary'

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is: $6.35x_1 + 3.95x_2 + 9.82x_3$

## 4: List the constraints in symbolic notation
The constraints are:
- $0.95x_1 \geq 0$ (implicit, as $x_1 \geq 0$ and quality rating is a given)
- $0.55x_2 \geq 0$ (implicit, as $x_2 \geq 0$ and quality rating is a given)
- $0.72x_3 \geq 0$ (implicit, as $x_3 \geq 0$ and quality rating is a given)
- $0.95x_1 + 0.55x_2 \geq 24$
- $0.95x_1 + 0.55x_2 + 0.72x_3 \geq 16$
- $0.95x_1 + 0.72x_3 \leq 61$
- $0.95x_1 + 0.55x_2 + 0.72x_3 \leq 61$
- $x_1$ is an integer
- $x_2$ is an integer
- $x_3$ is an integer

## 5: Provide the symbolic representation in the required format
```json
{
'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Hank'), ('x3', 'hours worked by Mary')],
'objective_function': '6.35*x1 + 3.95*x2 + 9.82*x3',
'constraints': [
    '0.95*x1 + 0.55*x2 >= 24',
    '0.95*x1 + 0.55*x2 + 0.72*x3 >= 16',
    '0.95*x1 + 0.72*x3 <= 61',
    '0.95*x1 + 0.55*x2 + 0.72*x3 <= 61',
    'x1 >= 0 and x1 is an integer',
    'x2 >= 0 and x2 is an integer',
    'x3 >= 0 and x3 is an integer'
]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name='x1', lb=0, type=gurobi.GRB.INTEGER)  # hours worked by Paul
    x2 = model.addVar(name='x2', lb=0, type=gurobi.GRB.INTEGER)  # hours worked by Hank
    x3 = model.addVar(name='x3', lb=0, type=gurobi.GRB.INTEGER)  # hours worked by Mary

    # Define the objective function
    model.setObjective(6.35*x1 + 3.95*x2 + 9.82*x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(0.95*x1 + 0.55*x2 >= 24)
    model.addConstr(0.95*x1 + 0.55*x2 + 0.72*x3 >= 16)
    model.addConstr(0.95*x1 + 0.72*x3 <= 61)
    model.addConstr(0.95*x1 + 0.55*x2 + 0.72*x3 <= 61)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print('Objective: ', model.objVal)
        print('Hours worked by Paul: ', x1.varValue)
        print('Hours worked by Hank: ', x2.varValue)
        print('Hours worked by Mary: ', x3.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```