To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints in terms of these variables.

Let's define:
- \(x_1\) as the hours worked by Paul,
- \(x_2\) as the hours worked by Hank,
- \(x_3\) as the hours worked by Mary.

The work quality ratings are given as:
- For Paul: 0.95
- For Hank: 0.55
- For Mary: 0.72

The objective function to maximize is:
\[6.35x_1 + 3.95x_2 + 9.82x_3\]

The constraints are:
1. \(0.95x_1 + 0.55x_2 \geq 24\)
2. \(0.95x_1 + 0.55x_2 + 0.72x_3 \geq 16\)
3. \(0.95x_1 + 0.72x_3 \leq 61\)
4. \(0.95x_1 + 0.55x_2 + 0.72x_3 \leq 61\)
5. \(x_1, x_2, x_3\) must be non-fractional (integer).

In symbolic notation, the problem can be represented as:
```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'
  ]
}
```

To implement this problem in Gurobi, we can use the following Python code:

```python
from gurobipy import *

# Create a new model
m = Model("Work_Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Paul")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Hank")
x3 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Mary")

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

# Add constraints
m.addConstr(0.95*x1 + 0.55*x2 >= 24, "Min_Quality_Paul_Hank")
m.addConstr(0.95*x1 + 0.55*x2 + 0.72*x3 >= 16, "Min_Quality_All")
m.addConstr(0.95*x1 + 0.72*x3 <= 61, "Max_Quality_Paul_Mary")
m.addConstr(0.95*x1 + 0.55*x2 + 0.72*x3 <= 61, "Max_Quality_All")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Paul: {x1.x}")
    print(f"Hours worked by Hank: {x2.x}")
    print(f"Hours worked by Mary: {x3.x}")
else:
    print("No optimal solution found")
```