To solve the given optimization problem, we first need to understand and translate the natural language description into a symbolic representation. The variables in this problem are 'hours worked by Mary' and 'hours worked by Paul'. We can represent these symbolically as \(x_1\) and \(x_2\), respectively.

The objective function is to maximize \(4.13x_1 + 9.68x_2\).

Given the constraints:
- The total combined likelihood to quit index should be at least 14: \(6.58x_1 + 2.37x_2 \geq 14\).
- The total combined computer competence rating should be at least 31: \(6.32x_1 + 2.73x_2 \geq 31\).
- The constraint \(-9x_1 + x_2 \geq 0\).
- The total combined likelihood to quit index should not exceed 28: \(6.58x_1 + 2.37x_2 \leq 28\).
- The total combined computer competence rating should not exceed 46: \(6.32x_1 + 2.73x_2 \leq 46\).
- Both \(x_1\) and \(x_2\) must be non-negative integers (since they represent hours worked).

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Paul')],
    'objective_function': '4.13*x1 + 9.68*x2',
    'constraints': [
        '6.58*x1 + 2.37*x2 >= 14',
        '6.32*x1 + 2.73*x2 >= 31',
        '-9*x1 + x2 >= 0',
        '6.58*x1 + 2.37*x2 <= 28',
        '6.32*x1 + 2.73*x2 <= 46'
    ]
}
```

Now, let's write the Gurobi code to solve this problem:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(4.13*x1 + 9.68*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(6.58*x1 + 2.37*x2 >= 14, "likelihood_to_quit_index_min")
m.addConstr(6.32*x1 + 2.73*x2 >= 31, "computer_competence_rating_min")
m.addConstr(-9*x1 + x2 >= 0, "constraint_3")
m.addConstr(6.58*x1 + 2.37*x2 <= 28, "likelihood_to_quit_index_max")
m.addConstr(6.32*x1 + 2.73*x2 <= 46, "computer_competence_rating_max")

# Optimize model
m.optimize()

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