## Step 1: Define the variables and their corresponding natural language objects
Let's define the variables and their corresponding natural language objects:
- $x_0$ = hours worked by Jean
- $x_1$ = hours worked by Dale
- $x_2$ = hours worked by Ringo
- $x_3$ = hours worked by George

## Step 2: Define the objective function
The objective function to maximize is: $5x_0 + x_1 + 3x_2 + 2x_3$

## Step 3: Define the constraints
Constraints:
1. $9x_0 \leq 116$
2. $7x_0 \leq 104$
3. $7x_0 \leq 223$
4. $1x_1 \leq 116$
5. $2x_1 \leq 104$
6. $10x_1 \leq 223$
7. $10x_2 \leq 116$
8. $4x_2 \leq 104$
9. $4x_2 \leq 223$
10. $3x_3 \leq 116$
11. $2x_3 \leq 104$
12. $4x_3 \leq 223$
13. $7x_0 + 4x_2 \geq 14$
14. $4x_2 + 2x_3 \geq 26$
15. $2x_1 + 4x_2 \geq 25$
16. $7x_0 + 2x_1 \geq 14$
17. $7x_0 + 2x_3 \geq 13$
18. $10x_1 + 4x_3 \geq 47$
19. $10x_1 + 4x_2 \geq 33$
20. $7x_0 + 10x_1 + 4x_3 \geq 29$
21. $7x_0 + 4x_2 + 4x_3 \geq 29$
22. $7x_0 + 10x_1 + 4x_2 \geq 29$
23. $10x_1 + 4x_2 + 4x_3 \geq 29$
24. $7x_0 + 10x_1 + 4x_3 \geq 34$
25. $7x_0 + 4x_2 + 4x_3 \geq 34$
26. $7x_0 + 10x_1 + 4x_2 \geq 34$
27. $10x_1 + 4x_2 + 4x_3 \geq 34$
28. $7x_0 + 10x_1 + 4x_3 \geq 47$
29. $7x_0 + 4x_2 + 4x_3 \geq 47$
30. $7x_0 + 10x_1 + 4x_2 \geq 47$
31. $10x_1 + 4x_2 + 4x_3 \geq 47$
32. $7x_0 + 10x_1 + 4x_3 \geq 54$
33. $7x_0 + 4x_2 + 4x_3 \geq 54$
34. $7x_0 + 10x_1 + 4x_2 \geq 54$
35. $10x_1 + 4x_2 + 4x_3 \geq 54$
36. $1x_1 + 10x_2 \leq 33$
37. $9x_0 + 1x_1 \leq 110$
38. $10x_2 + 3x_3 \leq 115$
39. $9x_0 + 10x_2 \leq 31$
40. $9x_0 + 1x_1 + 10x_2 + 3x_3 \leq 31$
41. $4x_2 + 2x_3 \leq 55$
42. $2x_1 + 4x_2 + 2x_3 \leq 69$
43. $7x_0 + 2x_1 + 4x_2 \leq 87$
44. $7x_0 + 2x_1 + 2x_3 \leq 92$
45. $7x_0 + 4x_2 + 2x_3 \leq 87$
46. $7x_0 + 2x_1 + 4x_2 + 2x_3 \leq 87$
47. $4x_2 + 4x_3 \leq 131$
48. $10x_1 + 4x_3 \leq 76$
49. $10x_1 + 4x_2 \leq 103$
50. $7x_0 + 10x_1 + 4x_2 + 4x_3 \leq 103$
51. $x_3$ is an integer.

## Step 4: Write the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Jean'),
        ('x1', 'hours worked by Dale'),
        ('x2', 'hours worked by Ringo'),
        ('x3', 'hours worked by George')
    ],
    'objective_function': '5*x0 + x1 + 3*x2 + 2*x3',
    'constraints': [
        '9*x0 <= 116',
        '7*x0 <= 104',
        '7*x0 <= 223',
        '1*x1 <= 116',
        '2*x1 <= 104',
        '10*x1 <= 223',
        '10*x2 <= 116',
        '4*x2 <= 104',
        '4*x2 <= 223',
        '3*x3 <= 116',
        '2*x3 <= 104',
        '4*x3 <= 223',
        '7*x0 + 4*x2 >= 14',
        '4*x2 + 2*x3 >= 26',
        '2*x1 + 4*x2 >= 25',
        '7*x0 + 2*x1 >= 14',
        '7*x0 + 2*x3 >= 13',
        '10*x1 + 4*x3 >= 47',
        '10*x1 + 4*x2 >= 33',
        '7*x0 + 10*x1 + 4*x3 >= 29',
        '7*x0 + 4*x2 + 4*x3 >= 29',
        '7*x0 + 10*x1 + 4*x2 >= 29',
        '10*x1 + 4*x2 + 4*x3 >= 29',
        '7*x0 + 10*x1 + 4*x3 >= 34',
        '7*x0 + 4*x2 + 4*x3 >= 34',
        '7*x0 + 10*x1 + 4*x2 >= 34',
        '10*x1 + 4*x2 + 4*x3 >= 34',
        '7*x0 + 10*x1 + 4*x3 >= 47',
        '7*x0 + 4*x2 + 4*x3 >= 47',
        '7*x0 + 10*x1 + 4*x2 >= 47',
        '10*x1 + 4*x2 + 4*x3 >= 47',
        '7*x0 + 10*x1 + 4*x3 >= 54',
        '7*x0 + 4*x2 + 4*x3 >= 54',
        '7*x0 + 10*x1 + 4*x2 >= 54',
        '10*x1 + 4*x2 + 4*x3 >= 54',
        '1*x1 + 10*x2 <= 33',
        '9*x0 + 1*x1 <= 110',
        '10*x2 + 3*x3 <= 115',
        '9*x0 + 10*x2 <= 31',
        '9*x0 + 1*x1 + 10*x2 + 3*x3 <= 31',
        '4*x2 + 2*x3 <= 55',
        '2*x1 + 4*x2 + 2*x3 <= 69',
        '7*x0 + 2*x1 + 4*x2 <= 87',
        '7*x0 + 2*x1 + 2*x3 <= 92',
        '7*x0 + 4*x2 + 2*x3 <= 87',
        '7*x0 + 2*x1 + 4*x2 + 2*x3 <= 87',
        '4*x2 + 4*x3 <= 131',
        '10*x1 + 4*x3 <= 76',
        '10*x1 + 4*x2 <= 103',
        '7*x0 + 10*x1 + 4*x2 + 4*x3 <= 103'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name='x0', lb=0)  # hours worked by Jean
x1 = m.addVar(name='x1', lb=0)  # hours worked by Dale
x2 = m.addVar(name='x2', lb=0)  # hours worked by Ringo
x3 = m.addVar(name='x3', lb=0, integrality=1)  # hours worked by George

# Objective function
m.setObjective(5*x0 + x1 + 3*x2 + 2*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(9*x0 <= 116)
m.addConstr(7*x0 <= 104)
m.addConstr(7*x0 <= 223)
m.addConstr(1*x1 <= 116)
m.addConstr(2*x1 <= 104)
m.addConstr(10*x1 <= 223)
m.addConstr(10*x2 <= 116)
m.addConstr(4*x2 <= 104)
m.addConstr(4*x2 <= 223)
m.addConstr(3*x3 <= 116)
m.addConstr(2*x3 <= 104)
m.addConstr(4*x3 <= 223)
m.addConstr(7*x0 + 4*x2 >= 14)
m.addConstr(4*x2 + 2*x3 >= 26)
m.addConstr(2*x1 + 4*x2 >= 25)
m.addConstr(7*x0 + 2*x1 >= 14)
m.addConstr(7*x0 + 2*x3 >= 13)
m.addConstr(10*x1 + 4*x3 >= 47)
m.addConstr(10*x1 + 4*x2 >= 33)
m.addConstr(7*x0 + 10*x1 + 4*x3 >= 29)
m.addConstr(7*x0 + 4*x2 + 4*x3 >= 29)
m.addConstr(7*x0 + 10*x1 + 4*x2 >= 29)
m.addConstr(10*x1 + 4*x2 + 4*x3 >= 29)
m.addConstr(7*x0 + 10*x1 + 4*x3 >= 34)
m.addConstr(7*x0 + 4*x2 + 4*x3 >= 34)
m.addConstr(7*x0 + 10*x1 + 4*x2 >= 34)
m.addConstr(10*x1 + 4*x2 + 4*x3 >= 34)
m.addConstr(7*x0 + 10*x1 + 4*x3 >= 47)
m.addConstr(7*x0 + 4*x2 + 4*x3 >= 47)
m.addConstr(7*x0 + 10*x1 + 4*x2 >= 47)
m.addConstr(10*x1 + 4*x2 + 4*x3 >= 47)
m.addConstr(7*x0 + 10*x1 + 4*x3 >= 54)
m.addConstr(7*x0 + 4*x2 + 4*x3 >= 54)
m.addConstr(7*x0 + 10*x1 + 4*x2 >= 54)
m.addConstr(10*x1 + 4*x2 + 4*x3 >= 54)
m.addConstr(1*x1 + 10*x2 <= 33)
m.addConstr(9*x0 + 1*x1 <= 110)
m.addConstr(10*x2 + 3*x3 <= 115)
m.addConstr(9*x0 + 10*x2 <= 31)
m.addConstr(9*x0 + 1*x1 + 10*x2 + 3*x3 <= 31)
m.addConstr(4*x2 + 2*x3 <= 55)
m.addConstr(2*x1 + 4*x2 + 2*x3 <= 69)
m.addConstr(7*x0 + 2*x1 + 4*x2 <= 87)
m.addConstr(7*x0 + 2*x1 + 2*x3 <= 92)
m.addConstr(7*x0 + 4*x2 + 2*x3 <= 87)
m.addConstr(7*x0 + 2*x1 + 4*x2 + 2*x3 <= 87)
m.addConstr(4*x2 + 4*x3 <= 131)
m.addConstr(10*x1 + 4*x3 <= 76)
m.addConstr(10*x1 + 4*x2 <= 103)
m.addConstr(7*x0 + 10*x1 + 4*x2 + 4*x3 <= 103)

# Solve the model
m.optimize()

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