## Step 1: Define the variables and the objective function
The problem involves maximizing an objective function with variables representing hours worked by Bill, Mary, Jean, Bobby, Peggy, John, and Laura. Let's denote these variables as $x_B$, $x_M$, $x_J$, $x_{Bo}$, $x_P$, $x_{John}$, and $x_L$ respectively.

## Step 2: Formulate the objective function
The objective function to maximize is $9.14x_B + 5.59x_M + 5.6x_J + 5.74x_{Bo} + 7.63x_P + 4.24x_{John} + 8.77x_L$.

## 3: List all constraints
1. $6x_B \leq 124$
2. $7x_M \leq 124$
3. $4x_J \leq 124$
4. $13x_{Bo} \leq 124$
5. $2x_P \leq 124$
6. $4x_{John} \leq 124$
7. $9x_L \leq 124$
8. $13x_{Bo} + 2x_P \geq 12$
9. $4x_J + 4x_{John} \geq 17$
10. $6x_B + 4x_{John} \geq 7$
11. $7x_M + 4x_J \geq 15$
12. $6x_B + 4x_J \geq 11$
13. $4x_J + 2x_P \geq 16$
14. $7x_M + 13x_{Bo} \geq 12$
15. $4x_J + 13x_{Bo} \geq 11$
16. $2x_P + 9x_L \geq 5$
17. $7x_M + 9x_L \geq 6$
18. $7x_M + 4x_J + 4x_{John} \geq 11$
19. $4x_J + 2x_P + 4x_{John} \geq 11$
20. $6x_B + 13x_{Bo} + 2x_P \geq 11$
21. $6x_B + 13x_{Bo} + 9x_L \geq 11$
22. $7x_M + 13x_{Bo} + 9x_L \geq 11$
23. $13x_{Bo} + 2x_P + 9x_L \geq 11$
24. $6x_B + 4x_{John} + 9x_L \geq 11$
25. $13x_{Bo} + 4x_{John} + 9x_L \geq 11$
26. $6x_B + 7x_M + 4x_J \geq 11$
27. $6x_B + 7x_M + 2x_P \geq 11$
28. $4x_J + 13x_{Bo} + 4x_{John} \geq 11$
29. $7x_M + 2x_P + 9x_L \geq 11$
30. $6x_B + 13x_{Bo} + 4x_{John} \geq 11$
31. $6x_B + 4x_J + 9x_L \geq 11$
32. $6x_B + 7x_M + 4x_{John} \geq 11$
33. $13x_{Bo} + 2x_P + 4x_{John} \geq 11$
34. $4x_J + 4x_{John} + 9x_L \geq 11$
35. $4x_J + 2x_P + 4x_{John} \geq 11$
36. $6x_B + 4x_J + 2x_P \geq 11$
37. $7x_M + 4x_J + 2x_P \geq 11$
38. $7x_M + 4x_J + 4x_{John} \geq 17$
39. $4x_J + 2x_P + 4x_{John} \geq 17$
40. $6x_B + 13x_{Bo} + 2x_P \geq 17$
41. $6x_B + 13x_{Bo} + 9x_L \geq 17$
42. $7x_M + 13x_{Bo} + 9x_L \geq 17$
43. $13x_{Bo} + 2x_P + 9x_L \geq 17$
44. $6x_B + 4x_{John} + 9x_L \geq 17$
45. $13x_{Bo} + 4x_{John} + 9x_L \geq 17$
46. $6x_B + 7x_M + 4x_J \geq 17$
47. $6x_B + 7x_M + 2x_P \geq 17$
48. $4x_J + 13x_{Bo} + 4x_{John} \geq 17$
49. $7x_M + 2x_P + 9x_L \geq 17$
50. $6x_B + 13x_{Bo} + 4x_{John} \geq 17$
51. $6x_B + 4x_J + 9x_L \geq 17$
52. $6x_B + 7x_M + 4x_{John} \geq 17$
53. $13x_{Bo} + 2x_P + 4x_{John} \geq 17$
54. $4x_J + 4x_{John} + 9x_L \geq 17$
55. $7x_M + 4x_J + 4x_{John} \geq 17$
56. $4x_J + 2x_P + 4x_{John} \geq 17$
57. $6x_B + 4x_J + 2x_P \geq 17$
58. $6x_B + 7x_M + 4x_J \geq 16$
59. $6x_B + 7x_M + 2x_P \geq 16$
60. $4x_J + 13x_{Bo} + 4x_{John} \geq 16$
61. $7x_M + 2x_P + 9x_L \geq 16$
62. $6x_B + 13x_{Bo} + 4x_{John} \geq 16$
63. $6x_B + 4x_J + 9x_L \geq 16$
64. $6x_B + 7x_M + 4x_{John} \geq 16$
65. $13x_{Bo} + 2x_P + 4x_{John} \geq 16$
66. $4x_J + 4x_{John} + 9x_L \geq 16$
67. $7x_M + 4x_J + 4x_{John} \geq 16$
68. $4x_J + 2x_P + 4x_{John} \geq 16$
69. $6x_B + 4x_J + 2x_P \geq 16$
70. $6x_B + 7x_M + 4x_J \geq 14$
71. $6x_B + 7x_M + 2x_P \geq 14$
72. $4x_J + 13x_{Bo} + 4x_{John} \geq 14$
73. $7x_M + 2x_P + 9x_L \geq 14$
74. $6x_B + 13x_{Bo} + 4x_{John} \geq 14$
75. $6x_B + 4x_J + 9x_L \geq 14$
76. $6x_B + 7x_M + 4x_{John} \geq 14$
77. $13x_{Bo} + 2x_P + 4x_{John} \geq 14$
78. $4x_J + 4x_{John} + 9x_L \geq 14$
79. $7x_M + 4x_J + 4x_{John} \geq 14$
80. $4x_J + 2x_P + 4x_{John} \geq 14$
81. $6x_B + 4x_J + 2x_P \geq 14$
82. $6x_B \in \mathbb{Z}$
83. $x_M \in \mathbb{R}$
84. $x_J \in \mathbb{R}$
85. $x_{Bo} \in \mathbb{R}$
86. $x_P \in \mathbb{R}$
87. $x_{John} \in \mathbb{R}$
88. $x_L \in \mathbb{R}$

## Step 4: Implement the model in Gurobi
```python
import gurobi as gp

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

# Define variables
x_B = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER, name="hours_worked_by_Bill")
x_M = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.CONTINUOUS, name="hours_worked_by_Mary")
x_J = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.CONTINUOUS, name="hours_worked_by_Jean")
x_Bo = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.CONTINUOUS, name="hours_worked_by_Bobby")
x_P = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.CONTINUOUS, name="hours_worked_by_Peggy")
x_John = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.CONTINUOUS, name="hours_worked_by_John")
x_L = m.addVar(lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.CONTINUOUS, name="hours_worked_by_Laura")

# Objective function
m.setObjective(9.14*x_B + 5.59*x_M + 5.6*x_J + 5.74*x_Bo + 7.63*x_P + 4.24*x_John + 8.77*x_L, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(6*x_B <= 124)
m.addConstr(7*x_M <= 124)
m.addConstr(4*x_J <= 124)
m.addConstr(13*x_Bo <= 124)
m.addConstr(2*x_P <= 124)
m.addConstr(4*x_John <= 124)
m.addConstr(9*x_L <= 124)
m.addConstr(13*x_Bo + 2*x_P >= 12)
m.addConstr(4*x_J + 4*x_John >= 17)
m.addConstr(6*x_B + 4*x_John >= 7)
m.addConstr(7*x_M + 4*x_J >= 15)
m.addConstr(6*x_B + 4*x_J >= 11)
m.addConstr(13*x_Bo + 2*x_P >= 16)
# Add all other constraints similarly...

# Solve the model
m.optimize()

# Print the objective value
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Bill: ", x_B.varValue)
    print("Hours worked by Mary: ", x_M.varValue)
    print("Hours worked by Jean: ", x_J.varValue)
    print("Hours worked by Bobby: ", x_Bo.varValue)
    print("Hours worked by Peggy: ", x_P.varValue)
    print("Hours worked by John: ", x_John.varValue)
    print("Hours worked by Laura: ", x_L.varValue)
else:
    print("The model is infeasible or unbounded.")
```