## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Paul' and 'hours worked by Hank'. Let's denote 'hours worked by Paul' as $x_1$ and 'hours worked by Hank' as $x_2$. The objective function to maximize is $8x_1 + 8x_2$.

## Step 2: List the constraints
The constraints given are:
- $14.64x_1 + 0.84x_2 \geq 58$
- $7.43x_1 + 6.44x_2 \geq 85$
- $22.05x_1 + 15.58x_2 \geq 107$
- $2.11x_1 + 20.34x_2 \geq 93$
- $7.51x_1 + 9.68x_2 \geq 94$
- $x_1 - 8x_2 \geq 0$
- $14.64x_1 + 0.84x_2 \leq 157$
- $7.43x_1 + 6.44x_2 \leq 144$
- $22.05x_1 + 15.58x_2 \leq 242$
- $2.11x_1 + 20.34x_2 \leq 344$
- $7.51x_1 + 9.68x_2 \leq 309$

## 3: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ['x1', 'hours worked by Paul'],
        ['x2', 'hours worked by Hank']
    ],
    'objective_function': '8*x1 + 8*x2',
    'constraints': [
        '14.64*x1 + 0.84*x2 >= 58',
        '7.43*x1 + 6.44*x2 >= 85',
        '22.05*x1 + 15.58*x2 >= 107',
        '2.11*x1 + 20.34*x2 >= 93',
        '7.51*x1 + 9.68*x2 >= 94',
        'x1 - 8*x2 >= 0',
        '14.64*x1 + 0.84*x2 <= 157',
        '7.43*x1 + 6.44*x2 <= 144',
        '22.05*x1 + 15.58*x2 <= 242',
        '2.11*x1 + 20.34*x2 <= 344',
        '7.51*x1 + 9.68*x2 <= 309'
    ]
}
```

## 4: Write the Gurobi code
```python
import gurobi

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

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

    # Define the objective function
    model.setObjective(8*x1 + 8*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(14.64*x1 + 0.84*x2 >= 58)
    model.addConstr(7.43*x1 + 6.44*x2 >= 85)
    model.addConstr(22.05*x1 + 15.58*x2 >= 107)
    model.addConstr(2.11*x1 + 20.34*x2 >= 93)
    model.addConstr(7.51*x1 + 9.68*x2 >= 94)
    model.addConstr(x1 - 8*x2 >= 0)
    model.addConstr(14.64*x1 + 0.84*x2 <= 157)
    model.addConstr(7.43*x1 + 6.44*x2 <= 144)
    model.addConstr(22.05*x1 + 15.58*x2 <= 242)
    model.addConstr(2.11*x1 + 20.34*x2 <= 344)
    model.addConstr(7.51*x1 + 9.68*x2 <= 309)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```