## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Mary' and 'hours worked by Hank'. Let's denote 'hours worked by Mary' as $x_1$ and 'hours worked by Hank' as $x_2$. The objective function to minimize is $4.58x_1 + 4.72x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
1. $14x_1 + 3x_2 \geq 95$
2. $13x_1 + 9x_2 \geq 47$
3. $5x_1 - 4x_2 \geq 0$
4. $14x_1 + 3x_2 \leq 127$
5. $13x_1 + 9x_2 \leq 75$

## 3: Define the symbolic representation
The symbolic variables are:
- $x_1$ for 'hours worked by Mary'
- $x_2$ for 'hours worked by Hank'

The objective function is: $4.58x_1 + 4.72x_2$

The constraints are:
1. $14x_1 + 3x_2 \geq 95$
2. $13x_1 + 9x_2 \geq 47$
3. $5x_1 - 4x_2 \geq 0$
4. $14x_1 + 3x_2 \leq 127$
5. $13x_1 + 9x_2 \leq 75$

## 4: Convert the problem into a Gurobi model
We will use Gurobi to solve this linear programming problem.

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="hours_worked_by_Mary", lb=0)  # Lower bound is 0, assuming hours cannot be negative
x2 = model.addVar(name="hours_worked_by_Hank", lb=0)   # Lower bound is 0, assuming hours cannot be negative

# Define the objective function
model.setObjective(4.58 * x1 + 4.72 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(14 * x1 + 3 * x2 >= 95)
model.addConstr(13 * x1 + 9 * x2 >= 47)
model.addConstr(5 * x1 - 4 * x2 >= 0)
model.addConstr(14 * x1 + 3 * x2 <= 127)
model.addConstr(13 * x1 + 9 * x2 <= 75)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Mary: {x1.varValue}")
    print(f"Hours worked by Hank: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Hank')],
    'objective_function': '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'
    ]
}
```

```python
import gurobi

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

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

    # Define the objective function
    model.setObjective(4.58 * x1 + 4.72 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(14 * x1 + 3 * x2 >= 95)
    model.addConstr(13 * x1 + 9 * x2 >= 47)
    model.addConstr(5 * x1 - 4 * x2 >= 0)
    model.addConstr(14 * x1 + 3 * x2 <= 127)
    model.addConstr(13 * x1 + 9 * x2 <= 75)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Mary: {x1.varValue}")
        print(f"Hours worked by Hank: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```