To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables and expressing the objective function and constraints using these variables.

Let's define the variables:
- $x_1$ represents the hours worked by Mary.
- $x_2$ represents the hours worked by Hank.

The objective function is given as: minimize $4.58x_1 + 4.72x_2$.

Now, let's list out the constraints based on the description provided:
1. The total combined productivity rating from hours worked by Mary and Hank must be 95 or more: $14x_1 + 3x_2 \geq 95$.
2. (This constraint is a repeat of the first, so we'll ignore it to avoid redundancy.)
3. The total combined likelihood to quit index from hours worked by Mary and Hank should be at minimum 47: $13x_1 + 9x_2 \geq 47$.
4. (This constraint is also a repeat, focusing on the same aspect as constraint 3, so it will be ignored for redundancy.)
5. $5x_1 - 4x_2 \geq 0$.
6. The total combined productivity rating from hours worked by Mary and Hank should be as much or less than 127: $14x_1 + 3x_2 \leq 127$.
7. The total combined likelihood to quit index from hours worked by Mary and Hank must be 75 or less: $13x_1 + 9x_2 \leq 75$.

Given these variables, objective function, and constraints, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Hank')],
  'objective_function': 'minimize 4.58*x1 + 4.72*x2',
  'constraints': [
    '14*x1 + 3*x2 >= 95',
    '13*x1 + 9*x2 >= 47',
    '5*x1 - 4*x2 >= 0',
    '14*x1 + 3*x2 <= 127',
    '13*x1 + 9*x2 <= 75'
  ]
}
```

Now, let's implement this problem using Gurobi in Python:
```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, name="hours_worked_by_Mary")
x2 = m.addVar(lb=0, name="hours_worked_by_Hank")

# Set the objective function
m.setObjective(4.58*x1 + 4.72*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(14*x1 + 3*x2 >= 95, name="productivity_rating_constraint")
m.addConstr(13*x1 + 9*x2 >= 47, name="quit_index_lower_bound")
m.addConstr(5*x1 - 4*x2 >= 0, name="mixed_constraint")
m.addConstr(14*x1 + 3*x2 <= 127, name="productivity_rating_upper_bound")
m.addConstr(13*x1 + 9*x2 <= 75, name="quit_index_upper_bound")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Hours worked by Mary:", x1.x)
    print("Hours worked by Hank:", x2.x)
else:
    print("No optimal solution found. Status:", m.status)
```