## Step 1: Define the variables and their corresponding natural language objects
The variables are 'hours worked by Jean', 'hours worked by Peggy', 'hours worked by Bill', 'hours worked by Hank', 'hours worked by Bobby'. Let's denote them as $x_0, x_1, x_2, x_3, x_4$ respectively.

## Step 2: Define the objective function
The objective function to maximize is $1.23x_0 + 5.77x_1 + 2.39x_2 + 7.61x_3 + 2.8x_4$.

## Step 3: List all the constraints
1. $x_0 \geq 0$, $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$, $x_4 \geq 0$ (non-negativity constraints, but since hours can be fractional, we consider them as continuous variables).
2. $12x_0 = 12$ (Jean's organization score),
3. $6x_0 = 6$ (Jean's dollar cost per hour),
4. $2x_0 = 2$ (Jean's likelihood to quit index),
5. $4x_1 = 4$ (Peggy's organization score),
6. $7x_1 = 7$ (Peggy's dollar cost per hour),
7. $8x_1 = 8$ (Peggy's likelihood to quit index),
8. $3x_2 = 3$ (Bill's organization score),
9. $9x_2 = 9$ (Bill's dollar cost per hour),
10. $3x_2 = 3$ (Bill's likelihood to quit index),
11. $11x_3 = 11$ (Hank's organization score),
12. $9x_3 = 9$ (Hank's dollar cost per hour),
13. $2x_3 = 2$ (Hank's likelihood to quit index),
14. $12x_4 = 12$ (Bobby's organization score),
15. $13x_4 = 13$ (Bobby's dollar cost per hour),
16. $6x_4 = 6$ (Bobby's likelihood to quit index),
17. $9x_3 + 13x_4 \geq 15$,
18. $6x_0 + 9x_3 + 13x_4 \geq 18$,
19. $2x_0 + 2x_3 \geq 30$,
20. $8x_1 + 3x_2 \geq 56$,
21. $3x_2 + 2x_3 \geq 23$,
22. $8x_1 + 6x_4 \geq 22$,
23. $2x_0 + 8x_1 \geq 31$,
24. $12x_0 + 4x_1 \leq 60$,
25. $12x_0 + 12x_4 \leq 72$,
26. $12x_0 + 11x_3 \leq 84$,
27. $12x_0 + 3x_2 \leq 158$,
28. $11x_3 + 12x_4 \leq 100$,
29. $4x_1 + 11x_3 \leq 73$,
30. $3x_2 + 12x_4 \leq 92$,
31. $3x_2 + 11x_3 \leq 125$,
32. $4x_1 + 3x_2 \leq 46$,
33. $12x_0 + 3x_2 + 11x_3 \leq 36$,
34. $3x_2 + 11x_3 + 12x_4 \leq 125$,
35. $12x_0 + 4x_1 + 3x_2 \leq 87$,
36. $4x_1 + 11x_3 + 12x_4 \leq 95$,
37. $4x_1 + 3x_2 + 12x_4 \leq 121$,
38. $12x_0 + 4x_1 + 11x_3 \leq 156$,
39. $12x_0 + 4x_1 + 3x_2 + 11x_3 + 12x_4 \leq 156$,
40. $7x_1 + 9x_2 \leq 104$,
41. $6x_0 + 9x_2 \leq 62$,
42. $9x_2 + 9x_3 \leq 27$,
43. $7x_1 + 13x_4 \leq 37$,
44. $9x_2 + 9x_3 + 13x_4 \leq 87$,
45. $6x_0 + 9x_2 + 9x_3 \leq 37$,
46. $6x_0 + 7x_1 + 9x_3 \leq 104$,
47. $6x_0 + 7x_1 + 9x_2 + 9x_3 + 13x_4 \leq 104$,
48. $3x_2 + 2x_3 \leq 205$,
49. $2x_0 + 6x_4 \leq 278$,
50. $2x_0 + 3x_2 \leq 226$,
51. $2x_0 + 2x_3 \leq 179$,
52. $3x_2 + 6x_4 \leq 159$,
53. $2x_0 + 2x_3 + 6x_4 \leq 286$,
54. $8x_1 + 2x_3 + 6x_4 \leq 214$,
55. $3x_2 + 2x_3 + 6x_4 \leq 153$,
56. $2x_0 + 8x_1 + 3x_2 + 2x_3 + 6x_4 \leq 153$.

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

# Define the model
m = gurobi.Model()

# Define the variables
x = [m.addVar(lb=0, name=f'x{i}') for i in range(5)]

# Set the variable bounds based on given equalities
m.addConstr(x[0] == 1, name='jean_org')
m.addConstr(6 * x[0] == 6, name='jean_dollar')
m.addConstr(2 * x[0] == 2, name='jean_quit')

m.addConstr(x[1] == 1, name='peggy_org')
m.addConstr(7 * x[1] == 7, name='peggy_dollar')
m.addConstr(8 * x[1] == 8, name='peggy_quit')

m.addConstr(x[2] == 1, name='bill_org')
m.addConstr(9 * x[2] == 9, name='bill_dollar')
m.addConstr(3 * x[2] == 3, name='bill_quit')

m.addConstr(x[3] == 1, name='hank_org')
m.addConstr(9 * x[3] == 9, name='hank_dollar')
m.addConstr(2 * x[3] == 2, name='hank_quit')

m.addConstr(x[4] == 1, name='bobby_org')
m.addConstr(13 * x[4] == 13, name='bobby_dollar')
m.addConstr(6 * x[4] == 6, name='bobby_quit')

# Add constraints
m.addConstr(9 * x[3] + 13 * x[4] >= 15)
m.addConstr(6 * x[0] + 9 * x[3] + 13 * x[4] >= 18)
m.addConstr(2 * x[0] + 2 * x[3] >= 30)
m.addConstr(8 * x[1] + 3 * x[2] >= 56)
m.addConstr(3 * x[2] + 2 * x[3] >= 23)
m.addConstr(8 * x[1] + 6 * x[4] >= 22)
m.addConstr(2 * x[0] + 8 * x[1] >= 31)
m.addConstr(12 * x[0] + 4 * x[1] <= 60)
m.addConstr(12 * x[0] + 12 * x[4] <= 72)
m.addConstr(12 * x[0] + 11 * x[3] <= 84)
m.addConstr(12 * x[0] + 3 * x[2] <= 158)
m.addConstr(11 * x[3] + 12 * x[4] <= 100)
m.addConstr(4 * x[1] + 11 * x[3] <= 73)
m.addConstr(3 * x[2] + 12 * x[4] <= 92)
m.addConstr(3 * x[2] + 11 * x[3] <= 125)
m.addConstr(4 * x[1] + 3 * x[2] <= 46)
m.addConstr(12 * x[0] + 3 * x[2] + 11 * x[3] <= 36)
m.addConstr(3 * x[2] + 11 * x[3] + 12 * x[4] <= 125)
m.addConstr(12 * x[0] + 4 * x[1] + 3 * x[2] <= 87)
m.addConstr(4 * x[1] + 11 * x[3] + 12 * x[4] <= 95)
m.addConstr(4 * x[1] + 3 * x[2] + 12 * x[4] <= 121)
m.addConstr(12 * x[0] + 4 * x[1] + 11 * x[3] <= 156)
m.addConstr(12 * x[0] + 4 * x[1] + 3 * x[2] + 11 * x[3] + 12 * x[4] <= 156)
m.addConstr(7 * x[1] + 9 * x[2] <= 104)
m.addConstr(6 * x[0] + 9 * x[2] <= 62)
m.addConstr(9 * x[2] + 9 * x[3] <= 27)
m.addConstr(7 * x[1] + 13 * x[4] <= 37)
m.addConstr(9 * x[2] + 9 * x[3] + 13 * x[4] <= 87)
m.addConstr(6 * x[0] + 9 * x[2] + 9 * x[3] <= 37)
m.addConstr(6 * x[0] + 7 * x[1] + 9 * x[3] <= 104)
m.addConstr(6 * x[0] + 7 * x[1] + 9 * x[2] + 9 * x[3] + 13 * x[4] <= 104)
m.addConstr(3 * x[2] + 2 * x[3] <= 205)
m.addConstr(2 * x[0] + 6 * x[4] <= 278)
m.addConstr(2 * x[0] + 3 * x[2] <= 226)
m.addConstr(2 * x[0] + 2 * x[3] <= 179)
m.addConstr(3 * x[2] + 6 * x[4] <= 159)
m.addConstr(2 * x[0] + 2 * x[3] + 6 * x[4] <= 286)
m.addConstr(8 * x[1] + 2 * x[3] + 6 * x[4] <= 214)
m.addConstr(3 * x[2] + 2 * x[3] + 6 * x[4] <= 153)
m.addConstr(2 * x[0] + 8 * x[1] + 3 * x[2] + 2 * x[3] + 6 * x[4] <= 153)

# Objective function
m.setObjective(1.23 * x[0] + 5.77 * x[1] + 2.39 * x[2] + 7.61 * x[3] + 2.8 * x[4], gurobi.GRB.MAXIMIZE)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.Status.OPTIMAL:
    print('Objective: %s' % m.objVal)
    for i in range(5):
        print(f'x{i}: {x[i].x}')
else:
    print('No solution found')
```

## Step 5: Symbolic representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Jean'),
        ('x1', 'hours worked by Peggy'),
        ('x2', 'hours worked by Bill'),
        ('x3', 'hours worked by Hank'),
        ('x4', 'hours worked by Bobby')
    ],
    'objective_function': '1.23*x0 + 5.77*x1 + 2.39*x2 + 7.61*x3 + 2.8*x4',
    'constraints': [
        'x0 = 1',
        'x1 = 1',
        'x2 = 1',
        'x3 = 1',
        'x4 = 1',
        '9*x3 + 13*x4 >= 15',
        '6*x0 + 9*x3 + 13*x4 >= 18',
        '2*x0 + 2*x3 >= 30',
        '8*x1 + 3*x2 >= 56',
        '3*x2 + 2*x3 >= 23',
        '8*x1 + 6*x4 >= 22',
        '2*x0 + 8*x1 >= 31',
        '12*x0 + 4*x1 <= 60',
        '12*x0 + 12*x4 <= 72',
        '12*x0 + 11*x3 <= 84',
        '12*x0 + 3*x2 <= 158',
        '11*x3 + 12*x4 <= 100',
        '4*x1 + 11*x3 <= 73',
        '3*x2 + 12*x4 <= 92',
        '3*x2 + 11*x3 <= 125',
        '4*x1 + 3*x2 <= 46',
        '12*x0 + 3*x2 + 11*x3 <= 36',
        '3*x2 + 11*x3 + 12*x4 <= 125',
        '12*x0 + 4*x1 + 3*x2 <= 87',
        '4*x1 + 11*x3 + 12*x4 <= 95',
        '4*x1 + 3*x2 + 12*x4 <= 121',
        '12*x0 + 4*x1 + 11*x3 <= 156',
        '12*x0 + 4*x1 + 3*x2 + 11*x3 + 12*x4 <= 156',
        '7*x1 + 9*x2 <= 104',
        '6*x0 + 9*x2 <= 62',
        '9*x2 + 9*x3 <= 27',
        '7*x1 + 13*x4 <= 37',
        '9*x2 + 9*x3 + 13*x4 <= 87',
        '6*x0 + 9*x2 + 9*x3 <= 37',
        '6*x0 + 7*x1 + 9*x3 <= 104',
        '6*x0 + 7*x1 + 9*x2 + 9*x3 + 13*x4 <= 104',
        '3*x2 + 2*x3 <= 205',
        '2*x0 + 6*x4 <= 278',
        '2*x0 + 3*x2 <= 226',
        '2*x0 + 2*x3 <= 179',
        '3*x2 + 6*x4 <= 159',
        '2*x0 + 2*x3 + 6*x4 <= 286',
        '8*x1 + 2*x3 + 6*x4 <= 214',
        '3*x2 + 2*x3 + 6*x4 <= 153',
        '2*x0 + 8*x1 + 3*x2 + 2*x3 + 6*x4 <= 153'
    ]
}
```