## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Dale', 'hours worked by Hank', and 'hours worked by Bill', which can be represented as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $1 \cdot x_0 + 5 \cdot x_1 + 5 \cdot x_2$.

## Step 3: List the constraints in symbolic notation
Constraints:
1. $9x_0 \geq 9$,
2. $10x_0 \geq 10$,
3. $4x_0 \geq 4$,
4. $14x_0 \geq 14$,
5. $9x_0 \geq 9$,
6. $3x_1 \geq 3$,
7. $5x_1 \geq 5$,
8. $5x_1 \geq 5$,
9. $9x_1 \geq 9$,
10. $1x_1 \geq 1$,
11. $11x_2 \geq 11$,
12. $5x_2 \geq 5$,
13. $8x_2 \geq 8$,
14. $12x_2 \geq 12$,
15. $13x_2 \geq 13$,
16. $9x_0 + 3x_1 \geq 6$,
17. $9x_0 + 3x_1 + 11x_2 \geq 12$,
18. $5x_1 + 5x_2 \geq 19$,
19. $10x_0 + 5x_1 \geq 17$,
20. $10x_0 + 5x_1 + 5x_2 \geq 26$,
21. $4x_0 + 5x_1 + 8x_2 \geq 27$,
22. $14x_0 + 12x_2 \geq 5$,
23. $14x_0 + 9x_1 \geq 9$,
24. $9x_0 + 13x_2 \geq 8$,
25. $9x_0 + 1x_1 \geq 6$,
26. $3x_1 + 11x_2 \leq 41$,
27. $9x_0 + 3x_1 \leq 47$,
28. $9x_0 + 3x_1 + 11x_2 \leq 38$,
29. $10x_0 + 5x_2 \leq 37$,
30. $10x_0 + 5x_1 \leq 57$,
31. $10x_0 + 5x_1 + 5x_2 \leq 57$,
32. $5x_1 + 8x_2 \leq 103$,
33. $4x_0 + 5x_1 \leq 78$,
34. $4x_0 + 5x_1 + 8x_2 \leq 78$,
35. $14x_0 + 9x_1 \leq 21$,
36. $14x_0 + 12x_2 \leq 22$,
37. $14x_0 + 9x_1 + 12x_2 \leq 22$,
38. $9x_0 + 13x_2 \leq 43$,
39. $9x_0 + 1x_1 + 13x_2 \leq 43$.

## Step 4: Convert the problem into Gurobi code
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="x0", vtype=gp.GRB.INTEGER)  # hours worked by Dale
x1 = m.addVar(name="x1", vtype=gp.GRB.INTEGER)  # hours worked by Hank
x2 = m.addVar(name="x2", vtype=gp.GRB.INTEGER)  # hours worked by Bill

# Define the objective function
m.setObjective(x0 + 5 * x1 + 5 * x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(9 * x0 >= 9)
m.addConstr(10 * x0 >= 10)
m.addConstr(4 * x0 >= 4)
m.addConstr(14 * x0 >= 14)
m.addConstr(9 * x0 >= 9)

m.addConstr(3 * x1 >= 3)
m.addConstr(5 * x1 >= 5)
m.addConstr(5 * x1 >= 5)
m.addConstr(9 * x1 >= 9)
m.addConstr(1 * x1 >= 1)

m.addConstr(11 * x2 >= 11)
m.addConstr(5 * x2 >= 5)
m.addConstr(8 * x2 >= 8)
m.addConstr(12 * x2 >= 12)
m.addConstr(13 * x2 >= 13)

m.addConstr(9 * x0 + 3 * x1 >= 6)
m.addConstr(9 * x0 + 3 * x1 + 11 * x2 >= 12)
m.addConstr(5 * x1 + 5 * x2 >= 19)
m.addConstr(10 * x0 + 5 * x1 >= 17)
m.addConstr(10 * x0 + 5 * x1 + 5 * x2 >= 26)
m.addConstr(4 * x0 + 5 * x1 + 8 * x2 >= 27)
m.addConstr(14 * x0 + 12 * x2 >= 5)
m.addConstr(14 * x0 + 9 * x1 >= 9)
m.addConstr(9 * x0 + 13 * x2 >= 8)
m.addConstr(9 * x0 + 1 * x1 >= 6)

m.addConstr(3 * x1 + 11 * x2 <= 41)
m.addConstr(9 * x0 + 3 * x1 <= 47)
m.addConstr(9 * x0 + 3 * x1 + 11 * x2 <= 38)
m.addConstr(10 * x0 + 5 * x2 <= 37)
m.addConstr(10 * x0 + 5 * x1 <= 57)
m.addConstr(10 * x0 + 5 * x1 + 5 * x2 <= 57)
m.addConstr(5 * x1 + 8 * x2 <= 103)
m.addConstr(4 * x0 + 5 * x1 <= 78)
m.addConstr(4 * x0 + 5 * x1 + 8 * x2 <= 78)
m.addConstr(14 * x0 + 9 * x1 <= 21)
m.addConstr(14 * x0 + 12 * x2 <= 22)
m.addConstr(14 * x0 + 9 * x1 + 12 * x2 <= 22)
m.addConstr(9 * x0 + 13 * x2 <= 43)
m.addConstr(9 * x0 + 1 * x1 + 13 * x2 <= 43)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Dale: ", x0.varValue)
    print("Hours worked by Hank: ", x1.varValue)
    print("Hours worked by Bill: ", x2.varValue)
else:
    print("The model is infeasible")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Dale'), 
        ('x1', 'hours worked by Hank'), 
        ('x2', 'hours worked by Bill')
    ], 
    'objective_function': 'x0 + 5x1 + 5x2', 
    'constraints': [
        '9x0 >= 9',
        '10x0 >= 10',
        '4x0 >= 4',
        '14x0 >= 14',
        '9x0 >= 9',
        '3x1 >= 3',
        '5x1 >= 5',
        '5x1 >= 5',
        '9x1 >= 9',
        '1x1 >= 1',
        '11x2 >= 11',
        '5x2 >= 5',
        '8x2 >= 8',
        '12x2 >= 12',
        '13x2 >= 13',
        '9x0 + 3x1 >= 6',
        '9x0 + 3x1 + 11x2 >= 12',
        '5x1 + 5x2 >= 19',
        '10x0 + 5x1 >= 17',
        '10x0 + 5x1 + 5x2 >= 26',
        '4x0 + 5x1 + 8x2 >= 27',
        '14x0 + 12x2 >= 5',
        '14x0 + 9x1 >= 9',
        '9x0 + 13x2 >= 8',
        '9x0 + 1x1 >= 6',
        '3x1 + 11x2 <= 41',
        '9x0 + 3x1 <= 47',
        '9x0 + 3x1 + 11x2 <= 38',
        '10x0 + 5x2 <= 37',
        '10x0 + 5x1 <= 57',
        '10x0 + 5x1 + 5x2 <= 57',
        '5x1 + 8x2 <= 103',
        '4x0 + 5x1 <= 78',
        '4x0 + 5x1 + 8x2 <= 78',
        '14x0 + 9x1 <= 21',
        '14x0 + 12x2 <= 22',
        '14x0 + 9x1 + 12x2 <= 22',
        '9x0 + 13x2 <= 43',
        '9x0 + 1x1 + 13x2 <= 43'
    ]
}
```