## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by John', 'hours worked by Laura', 'hours worked by Hank', 'hours worked by Ringo']. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $9x_0 + 2x_1 + 5x_2 + 2x_3$.

## Step 3: List all the constraints in symbolic notation
1. $22x_0 \leq 256$
2. $32x_0 \leq 432$
3. $6x_1 \leq 256$
4. $9x_1 \leq 432$
5. $7x_2 \leq 256$
6. $28x_2 \leq 432$
7. $5x_3 \leq 256$
8. $28x_3 \leq 432$
9. $7x_2 + 5x_3 \geq 57$
10. $22x_0 + 5x_3 \geq 25$
11. $22x_0 + 6x_1 \geq 23$
12. $22x_0 + 7x_2 + 5x_3 \geq 41$
13. $22x_0 + 6x_1 + 7x_2 \geq 41$
14. $22x_0 + 7x_2 + 5x_3 \geq 45$
15. $22x_0 + 6x_1 + 7x_2 \geq 45$
16. $22x_0 + 6x_1 + 7x_2 + 5x_3 \geq 45$
17. $32x_0 + 9x_1 \geq 87$
18. $32x_0 + 28x_2 \geq 61$
19. $9x_1 + 28x_2 \geq 49$
20. $32x_0 + 9x_1 + 28x_2 + 28x_3 \geq 49$
21. $-8x_1 + 5x_3 \geq 0$
22. $-x_1 + 10x_2 \geq 0$
23. $22x_0 + 6x_1 + 7x_2 \leq 239$
24. $9x_1 + 28x_3 \leq 430$
25. $32x_0 + 28x_3 \leq 384$
26. $32x_0 + 9x_1 \leq 313$
27. $9x_1 + 28x_2 \leq 130$
28. $28x_2 + 28x_3 \leq 193$

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by John'), 
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by Hank'), 
        ('x3', 'hours worked by Ringo')
    ], 
    'objective_function': '9*x0 + 2*x1 + 5*x2 + 2*x3', 
    'constraints': [
        '22*x0 <= 256',
        '32*x0 <= 432',
        '6*x1 <= 256',
        '9*x1 <= 432',
        '7*x2 <= 256',
        '28*x2 <= 432',
        '5*x3 <= 256',
        '28*x3 <= 432',
        '7*x2 + 5*x3 >= 57',
        '22*x0 + 5*x3 >= 25',
        '22*x0 + 6*x1 >= 23',
        '22*x0 + 7*x2 + 5*x3 >= 41',
        '22*x0 + 6*x1 + 7*x2 >= 41',
        '22*x0 + 7*x2 + 5*x3 >= 45',
        '22*x0 + 6*x1 + 7*x2 >= 45',
        '22*x0 + 6*x1 + 7*x2 + 5*x3 >= 45',
        '32*x0 + 9*x1 >= 87',
        '32*x0 + 28*x2 >= 61',
        '9*x1 + 28*x2 >= 49',
        '32*x0 + 9*x1 + 28*x2 + 28*x3 >= 49',
        '-8*x1 + 5*x3 >= 0',
        '-x1 + 10*x2 >= 0',
        '22*x0 + 6*x1 + 7*x2 <= 239',
        '9*x1 + 28*x3 <= 430',
        '32*x0 + 28*x3 <= 384',
        '32*x0 + 9*x1 <= 313',
        '9*x1 + 28*x2 <= 130',
        '28*x2 + 28*x3 <= 193'
    ]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name='x0', lb=0)  # hours worked by John
    x1 = model.addVar(name='x1', lb=0)  # hours worked by Laura
    x2 = model.addVar(name='x2', lb=0)  # hours worked by Hank
    x3 = model.addVar(name='x3', lb=0)  # hours worked by Ringo

    # Define the objective function
    model.setObjective(9 * x0 + 2 * x1 + 5 * x2 + 2 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(22 * x0 <= 256)
    model.addConstr(32 * x0 <= 432)
    model.addConstr(6 * x1 <= 256)
    model.addConstr(9 * x1 <= 432)
    model.addConstr(7 * x2 <= 256)
    model.addConstr(28 * x2 <= 432)
    model.addConstr(5 * x3 <= 256)
    model.addConstr(28 * x3 <= 432)
    model.addConstr(7 * x2 + 5 * x3 >= 57)
    model.addConstr(22 * x0 + 5 * x3 >= 25)
    model.addConstr(22 * x0 + 6 * x1 >= 23)
    model.addConstr(22 * x0 + 7 * x2 + 5 * x3 >= 41)
    model.addConstr(22 * x0 + 6 * x1 + 7 * x2 >= 41)
    model.addConstr(22 * x0 + 7 * x2 + 5 * x3 >= 45)
    model.addConstr(22 * x0 + 6 * x1 + 7 * x2 >= 45)
    model.addConstr(22 * x0 + 6 * x1 + 7 * x2 + 5 * x3 >= 45)
    model.addConstr(32 * x0 + 9 * x1 >= 87)
    model.addConstr(32 * x0 + 28 * x2 >= 61)
    model.addConstr(9 * x1 + 28 * x2 >= 49)
    model.addConstr(32 * x0 + 9 * x1 + 28 * x2 + 28 * x3 >= 49)
    model.addConstr(-8 * x1 + 5 * x3 >= 0)
    model.addConstr(-x1 + 10 * x2 >= 0)
    model.addConstr(22 * x0 + 6 * x1 + 7 * x2 <= 239)
    model.addConstr(9 * x1 + 28 * x3 <= 430)
    model.addConstr(32 * x0 + 28 * x3 <= 384)
    model.addConstr(32 * x0 + 9 * x1 <= 313)
    model.addConstr(9 * x1 + 28 * x2 <= 130)
    model.addConstr(28 * x2 + 28 * x3 <= 193)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('x0: ', x0.varValue)
        print('x1: ', x1.varValue)
        print('x2: ', x2.varValue)
        print('x3: ', x3.varValue)
    else:
        print('No optimal solution found')

solve_optimization_problem()
```