## Step 1: Define the variables and their corresponding symbolic notation
The variables are: 
- hours worked by Paul
- hours worked by Bill
- hours worked by George
- hours worked by Hank
- hours worked by John
- hours worked by Ringo
- hours worked by Jean

Let's denote them as:
- $x_1$ for hours worked by Paul
- $x_2$ for hours worked by Bill
- $x_3$ for hours worked by George
- $x_4$ for hours worked by Hank
- $x_5$ for hours worked by John
- $x_6$ for hours worked by Ringo
- $x_7$ for hours worked by Jean

## Step 2: Formulate the objective function
The objective function to maximize is:
$6.63x_1 + 4.33x_2 + 2.22x_3 + 7.29x_4 + 2.29x_5 + 6.9x_6 + 1.01x_7$

## 3: List the constraints
1. $8x_1 \geq 0$ (Implicit, as $x_1 \geq 0$)
2. $11x_2 \geq 0$ (Implicit, as $x_2 \geq 0$)
3. $2x_3 \geq 0$ (Implicit, as $x_3 \geq 0$)
4. $2x_4 \geq 0$ (Implicit, as $x_4 \geq 0$)
5. $11x_5 \geq 0$ (Implicit, as $x_5 \geq 0$)
6. $6x_6 \geq 0$ (Implicit, as $x_6 \geq 0$)
7. $11x_7 \geq 0$ (Implicit, as $x_7 \geq 0$)
8. $2x_3 + 11x_7 \geq 13$
9. $8x_1 + 11x_5 \geq 22$
10. $2x_3 + 6x_6 \geq 12$
11. $11x_2 + 2x_4 \geq 28$
12. $11x_2 + 2x_3 \geq 13$
13. $2x_4 + 6x_6 \geq 20$
14. $6x_6 + 11x_7 \geq 17$
15. $8x_1 + 2x_4 \geq 26$
16. $11x_5 + 6x_6 \geq 27$
17. $8x_1 + 11x_7 \geq 11$
18. $2x_3 + 2x_4 \leq 183$
19. $2x_3 + 6x_6 \leq 198$
20. $11x_5 + 11x_7 \leq 96$
21. $6x_6 + 11x_7 \leq 33$
22. $11x_5 + 6x_6 \leq 167$
23. $8x_1 + 6x_6 \leq 71$
24. $2x_4 + 11x_5 \leq 64$
25. $2x_4 + 6x_6 \leq 52$
26. $8x_1 + 2x_4 \leq 138$
27. $8x_1 + 2x_3 \leq 49$
28. $11x_2 + 2x_3 \leq 36$
29. $11x_2 + 2x_3 + 2x_4 \leq 75$
30. $2x_3 + 2x_4 + 6x_6 \leq 165$
31. $2x_4 + 6x_6 + 11x_7 \leq 205$
32. $11x_2 + 2x_3 + 11x_5 \leq 93$
33. $8x_1 + 2x_4 + 6x_6 \leq 192$
34. $8x_1 + 11x_2 + 11x_7 \leq 101$
35. $2x_3 + 11x_5 + 11x_7 \leq 140$
36. $8x_1 + 6x_6 + 11x_7 \leq 208$
37. $2x_4 + 11x_5 + 11x_7 \leq 76$
38. $11x_2 + 11x_5 + 11x_7 \leq 151$
39. $8x_1 + 11x_2 + 2x_3 + 2x_4 + 11x_5 + 6x_6 + 11x_7 \leq 151$

## 4: Symbolic Representation
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Paul'),
        ('x2', 'hours worked by Bill'),
        ('x3', 'hours worked by George'),
        ('x4', 'hours worked by Hank'),
        ('x5', 'hours worked by John'),
        ('x6', 'hours worked by Ringo'),
        ('x7', 'hours worked by Jean')
    ],
    'objective_function': '6.63*x1 + 4.33*x2 + 2.22*x3 + 7.29*x4 + 2.29*x5 + 6.9*x6 + 1.01*x7',
    'constraints': [
        '2*x3 + 11*x7 >= 13',
        '8*x1 + 11*x5 >= 22',
        '2*x3 + 6*x6 >= 12',
        '11*x2 + 2*x4 >= 28',
        '11*x2 + 2*x3 >= 13',
        '2*x4 + 6*x6 >= 20',
        '6*x6 + 11*x7 >= 17',
        '8*x1 + 2*x4 >= 26',
        '11*x5 + 6*x6 >= 27',
        '8*x1 + 11*x7 >= 11',
        '2*x3 + 2*x4 <= 183',
        '2*x3 + 6*x6 <= 198',
        '11*x5 + 11*x7 <= 96',
        '6*x6 + 11*x7 <= 33',
        '11*x5 + 6*x6 <= 167',
        '8*x1 + 6*x6 <= 71',
        '2*x4 + 11*x5 <= 64',
        '2*x4 + 6*x6 <= 52',
        '8*x1 + 2*x4 <= 138',
        '8*x1 + 2*x3 <= 49',
        '11*x2 + 2*x3 <= 36',
        '11*x2 + 2*x3 + 2*x4 <= 75',
        '2*x3 + 2*x4 + 6*x6 <= 165',
        '2*x4 + 6*x6 + 11*x7 <= 205',
        '11*x2 + 2*x3 + 11*x5 <= 93',
        '8*x1 + 2*x4 + 6*x6 <= 192',
        '8*x1 + 11*x2 + 11*x7 <= 101',
        '2*x3 + 11*x5 + 11*x7 <= 140',
        '8*x1 + 6*x6 + 11*x7 <= 208',
        '2*x4 + 11*x5 + 11*x7 <= 76',
        '11*x2 + 11*x5 + 11*x7 <= 151',
        '8*x1 + 11*x2 + 2*x3 + 2*x4 + 11*x5 + 6*x6 + 11*x7 <= 151'
    ]
}
```

## 5: Gurobi Code
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='x1', lb=0)  # hours worked by Paul
    x2 = model.addVar(name='x2', lb=0)  # hours worked by Bill
    x3 = model.addVar(name='x3', lb=0)  # hours worked by George
    x4 = model.addVar(name='x4', lb=0)  # hours worked by Hank
    x5 = model.addVar(name='x5', lb=0)  # hours worked by John
    x6 = model.addVar(name='x6', lb=0)  # hours worked by Ringo
    x7 = model.addVar(name='x7', lb=0)  # hours worked by Jean

    # Objective function
    model.setObjective(6.63*x1 + 4.33*x2 + 2.22*x3 + 7.29*x4 + 2.29*x5 + 6.9*x6 + 1.01*x7, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2*x3 + 11*x7 >= 13)
    model.addConstr(8*x1 + 11*x5 >= 22)
    model.addConstr(2*x3 + 6*x6 >= 12)
    model.addConstr(11*x2 + 2*x4 >= 28)
    model.addConstr(11*x2 + 2*x3 >= 13)
    model.addConstr(2*x4 + 6*x6 >= 20)
    model.addConstr(6*x6 + 11*x7 >= 17)
    model.addConstr(8*x1 + 2*x4 >= 26)
    model.addConstr(11*x5 + 6*x6 >= 27)
    model.addConstr(8*x1 + 11*x7 >= 11)
    model.addConstr(2*x3 + 2*x4 <= 183)
    model.addConstr(2*x3 + 6*x6 <= 198)
    model.addConstr(11*x5 + 11*x7 <= 96)
    model.addConstr(6*x6 + 11*x7 <= 33)
    model.addConstr(11*x5 + 6*x6 <= 167)
    model.addConstr(8*x1 + 6*x6 <= 71)
    model.addConstr(2*x4 + 11*x5 <= 64)
    model.addConstr(2*x4 + 6*x6 <= 52)
    model.addConstr(8*x1 + 2*x4 <= 138)
    model.addConstr(8*x1 + 2*x3 <= 49)
    model.addConstr(11*x2 + 2*x3 <= 36)
    model.addConstr(11*x2 + 2*x3 + 2*x4 <= 75)
    model.addConstr(2*x3 + 2*x4 + 6*x6 <= 165)
    model.addConstr(2*x4 + 6*x6 + 11*x7 <= 205)
    model.addConstr(11*x2 + 2*x3 + 11*x5 <= 93)
    model.addConstr(8*x1 + 2*x4 + 6*x6 <= 192)
    model.addConstr(8*x1 + 11*x2 + 11*x7 <= 101)
    model.addConstr(2*x3 + 11*x5 + 11*x7 <= 140)
    model.addConstr(8*x1 + 6*x6 + 11*x7 <= 208)
    model.addConstr(2*x4 + 11*x5 + 11*x7 <= 76)
    model.addConstr(11*x2 + 11*x5 + 11*x7 <= 151)
    model.addConstr(8*x1 + 11*x2 + 2*x3 + 2*x4 + 11*x5 + 6*x6 + 11*x7 <= 151)

    # Optimize the model
    model.optimize()

    # Print the objective value
    print('Objective value:', model.objVal)

    # Print the variable values
    print('x1:', x1.varValue)
    print('x2:', x2.varValue)
    print('x3:', x3.varValue)
    print('x4:', x4.varValue)
    print('x5:', x5.varValue)
    print('x6:', x6.varValue)
    print('x7:', x7.varValue)

optimization_problem()
```