## Step 1: Define the variables and resources
We have five variables: 
- $x_0$: hours worked by Laura
- $x_1$: hours worked by Bobby
- $x_2$: hours worked by Peggy
- $x_3$: hours worked by Dale
- $x_4$: hours worked by John

And two resources/attributes:
- $r_0$: productivity rating
- $r_1$: organization score

With the following values:
- $r_0$: {'x0': 9, 'x1': 15, 'x2': 6, 'x3': 20, 'x4': 17}
- $r_1$: {'x0': 19, 'x1': 5, 'x2': 11, 'x3': 11, 'x4': 6}

## Step 2: Formulate the objective function
The objective function to maximize is: $5x_0 + 7x_1 + x_2 + 3x_3 + 6x_4$

## Step 3: List all constraints
1. $9x_0 \geq 9 \cdot x_0$ (always true, so redundant)
2. $19x_0 \geq 19 \cdot x_0$ (always true, so redundant)
3. $15x_1 \geq 15 \cdot x_1$ (always true, so redundant)
4. $5x_1 \geq 5 \cdot x_1$ (always true, so redundant)
5. $6x_2 \geq 6 \cdot x_2$ (always true, so redundant)
6. $11x_2 \geq 11 \cdot x_2$ (always true, so redundant)
7. $20x_3 \geq 20 \cdot x_3$ (always true, so redundant)
8. $11x_3 \geq 11 \cdot x_3$ (always true, so redundant)
9. $17x_4 \geq 17 \cdot x_4$ (always true, so redundant)
10. $6x_4 \geq 6 \cdot x_4$ (always true, so redundant)
11. $9x_0 + 20x_3 \geq 57$
12. $6x_2 + 17x_4 \geq 62$
13. $9x_0 + 17x_4 \geq 53$
14. $9x_0 + 6x_2 + 17x_4 \geq 44$
15. $15x_1 + 6x_2 + 17x_4 \geq 44$
16. $15x_1 + 20x_3 + 17x_4 \geq 44$
17. $6x_2 + 20x_3 + 17x_4 \geq 44$
18. $9x_0 + 6x_2 + 17x_4 \geq 54$
19. $15x_1 + 6x_2 + 17x_4 \geq 54$
20. $15x_1 + 20x_3 + 17x_4 \geq 54$
21. $6x_2 + 20x_3 + 17x_4 \geq 54$
22. $9x_0 + 6x_2 + 17x_4 \geq 50$
23. $15x_1 + 6x_2 + 17x_4 \geq 50$
24. $15x_1 + 20x_3 + 17x_4 \geq 50$
25. $6x_2 + 20x_3 + 17x_4 \geq 50$
26. $9x_0 + 6x_2 + 17x_4 \geq 60$
27. $15x_1 + 6x_2 + 17x_4 \geq 60$
28. $15x_1 + 20x_3 + 17x_4 \geq 60$
29. $6x_2 + 20x_3 + 17x_4 \geq 60$
30. $5x_1 + 11x_2 \geq 150$
31. $19x_0 + 11x_3 \geq 75$
32. $19x_0 + 6x_4 \geq 104$
33. $5x_1 + 11x_3 \geq 117$
34. $19x_0 + 5x_1 \geq 79$
35. $19x_0 + 5x_1 + 11x_3 \geq 147$
36. $19x_0 + 11x_2 + 11x_3 \geq 147$
37. $11x_2 + 11x_3 + 6x_4 \geq 147$
38. $5x_1 + 11x_2 + 11x_3 \geq 147$
39. $19x_0 + 11x_2 + 6x_4 \geq 147$
40. $5x_1 + 11x_2 + 6x_4 \geq 147$
41. $19x_0 + 5x_1 + 11x_2 \geq 147$
42. $19x_0 + 11x_3 + 6x_4 \geq 147$
43. $19x_0 + 5x_1 + 11x_3 \geq 109$
44. $19x_0 + 11x_2 + 11x_3 \geq 109$
45. $11x_2 + 11x_3 + 6x_4 \geq 109$
46. $5x_1 + 11x_2 + 11x_3 \geq 109$
47. $19x_0 + 11x_2 + 6x_4 \geq 109$
48. $5x_1 + 11x_2 + 6x_4 \geq 109$
49. $19x_0 + 5x_1 + 11x_2 \geq 109$
50. $19x_0 + 11x_3 + 6x_4 \geq 109$
51. $5x_1 + 5x_1 - 3x_2 \geq 0$
52. $9x_0 + 17x_4 \leq 171$
53. $15x_1 + 20x_3 \leq 120$
54. $9x_0 + 15x_1 + 6x_2 + 20x_3 + 17x_4 \leq 120$
55. $19x_0 + 11x_2 \leq 411$
56. $11x_2 + 11x_3 \leq 276$
57. $5x_1 + 6x_4 \leq 422$
58. $11x_3 + 6x_4 \leq 268$
59. $5x_1 + 11x_3 \leq 409$
60. $11x_2 + 6x_4 \leq 688$
61. $19x_0 + 5x_1 + 11x_2 + 11x_3 + 6x_4 \leq 688$

## Step 4: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="hours_worked_by_Laura", lb=0)
x1 = m.addVar(name="hours_worked_by_Bobby", lb=0)
x2 = m.addVar(name="hours_worked_by_Peggy", lb=0)
x3 = m.addVar(name="hours_worked_by_Dale", lb=0)
x4 = m.addVar(name="hours_worked_by_John", lb=0)

# Define the objective function
m.setObjective(5 * x0 + 7 * x1 + x2 + 3 * x3 + 6 * x4, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(9 * x0 + 20 * x3 >= 57)
m.addConstr(6 * x2 + 17 * x4 >= 62)
m.addConstr(9 * x0 + 17 * x4 >= 53)
m.addConstr(9 * x0 + 6 * x2 + 17 * x4 >= 44)
m.addConstr(15 * x1 + 6 * x2 + 17 * x4 >= 44)
m.addConstr(15 * x1 + 20 * x3 + 17 * x4 >= 44)
m.addConstr(6 * x2 + 20 * x3 + 17 * x4 >= 44)
m.addConstr(9 * x0 + 6 * x2 + 17 * x4 >= 54)
m.addConstr(15 * x1 + 6 * x2 + 17 * x4 >= 54)
m.addConstr(15 * x1 + 20 * x3 + 17 * x4 >= 54)
m.addConstr(6 * x2 + 20 * x3 + 17 * x4 >= 54)
m.addConstr(9 * x0 + 6 * x2 + 17 * x4 >= 50)
m.addConstr(15 * x1 + 6 * x2 + 17 * x4 >= 50)
m.addConstr(15 * x1 + 20 * x3 + 17 * x4 >= 50)
m.addConstr(6 * x2 + 20 * x3 + 17 * x4 >= 50)
m.addConstr(9 * x0 + 6 * x2 + 17 * x4 >= 60)
m.addConstr(15 * x1 + 6 * x2 + 17 * x4 >= 60)
m.addConstr(15 * x1 + 20 * x3 + 17 * x4 >= 60)
m.addConstr(6 * x2 + 20 * x3 + 17 * x4 >= 60)
m.addConstr(5 * x1 + 11 * x2 >= 150)
m.addConstr(19 * x0 + 11 * x3 >= 75)
m.addConstr(19 * x0 + 6 * x4 >= 104)
m.addConstr(5 * x1 + 11 * x3 >= 117)
m.addConstr(19 * x0 + 5 * x1 >= 79)
m.addConstr(19 * x0 + 5 * x1 + 11 * x3 >= 147)
m.addConstr(19 * x0 + 11 * x2 + 11 * x3 >= 147)
m.addConstr(11 * x2 + 11 * x3 + 6 * x4 >= 147)
m.addConstr(5 * x1 + 11 * x2 + 11 * x3 >= 147)
m.addConstr(19 * x0 + 11 * x2 + 6 * x4 >= 147)
m.addConstr(5 * x1 + 11 * x2 + 6 * x4 >= 147)
m.addConstr(19 * x0 + 5 * x1 + 11 * x2 >= 147)
m.addConstr(19 * x0 + 11 * x3 + 6 * x4 >= 147)
m.addConstr(5 * x1 - 3 * x2 >= 0)
m.addConstr(9 * x0 + 17 * x4 <= 171)
m.addConstr(15 * x1 + 20 * x3 <= 120)
m.addConstr(9 * x0 + 15 * x1 + 6 * x2 + 20 * x3 + 17 * x4 <= 120)
m.addConstr(19 * x0 + 11 * x2 <= 411)
m.addConstr(11 * x2 + 11 * x3 <= 276)
m.addConstr(5 * x1 + 6 * x4 <= 422)
m.addConstr(11 * x3 + 6 * x4 <= 268)
m.addConstr(5 * x1 + 11 * x3 <= 409)
m.addConstr(11 * x2 + 6 * x4 <= 688)
m.addConstr(19 * x0 + 5 * x1 + 11 * x2 + 11 * x3 + 6 * x4 <= 688)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Laura: ", x0.varValue)
    print("Hours worked by Bobby: ", x1.varValue)
    print("Hours worked by Peggy: ", x2.varValue)
    print("Hours worked by Dale: ", x3.varValue)
    print("Hours worked by John: ", x4.varValue)
else:
    print("The model is infeasible")
```