## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. Let's define the symbolic variables:
- $x_0$ for 'hours worked by Bobby'
- $x_1$ for 'hours worked by Mary'
- $x_2$ for 'hours worked by George'

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $5.96x_0 + 7.76x_1 + 5.99x_2$.

## 3: List the constraints in symbolic notation
1. $8x_0 \leq 85$ (work quality rating for Bobby)
2. $8x_0 \leq 170$ (dollar cost per hour for Bobby)
3. $2x_0 \leq 87$ (paperwork competence rating for Bobby)
4. $6x_0 \leq 87$ (likelihood to quit index for Bobby)
5. $5x_1 \leq 85$ (work quality rating for Mary)
6. $3x_1 \leq 170$ (dollar cost per hour for Mary)
7. $x_1 \leq 87$ (paperwork competence rating for Mary)
8. $8x_1 \leq 87$ (likelihood to quit index for Mary)
9. $2x_2 \leq 85$ (work quality rating for George)
10. $3x_2 \leq 170$ (dollar cost per hour for George)
11. $7x_2 \leq 87$ (paperwork competence rating for George)
12. $8x_2 \leq 87$ (likelihood to quit index for George)
13. $5x_1 + 2x_2 \geq 15$ (total combined work quality rating from Mary and George)
14. $8x_0 + 5x_1 \geq 22$ (total combined work quality rating from Bobby and Mary)
15. $8x_0 + 5x_1 \leq 75$ (total combined work quality rating from Bobby and Mary)
16. $8x_0 + 2x_2 \leq 61$ (total combined work quality rating from Bobby and George)
17. $8x_0 + 5x_1 + 2x_2 \leq 61$ (total combined work quality rating from all)
18. $8x_0 + 3x_2 \leq 102$ (total combined dollar cost per hour from Bobby and George)
19. $8x_0 + 3x_1 \leq 134$ (total combined dollar cost per hour from Bobby and Mary)
20. $8x_0 + 3x_1 + 3x_2 \leq 158$ (total combined dollar cost per hour from all)
21. $x_1 + 7x_2 \leq 35$ (total combined paperwork competence rating from Mary and George)
22. $2x_0 + x_1 \leq 48$ (total combined paperwork competence rating from Bobby and Mary)
23. $2x_0 + x_1 + 7x_2 \leq 48$ (total combined paperwork competence rating from all)
24. $8x_1 + 8x_2 \leq 69$ (total combined likelihood to quit index from Mary and George)
25. $6x_0 + 8x_2 \leq 50$ (total combined likelihood to quit index from Bobby and George)
26. $6x_0 + 8x_1 + 8x_2 \leq 84$ (total combined likelihood to quit index from all)

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x0', 'hours worked by Bobby'), ('x1', 'hours worked by Mary'), ('x2', 'hours worked by George')],
    'objective_function': '5.96*x0 + 7.76*x1 + 5.99*x2',
    'constraints': [
        '8*x0 <= 85',
        '8*x0 <= 170',
        '2*x0 <= 87',
        '6*x0 <= 87',
        '5*x1 <= 85',
        '3*x1 <= 170',
        'x1 <= 87',
        '8*x1 <= 87',
        '2*x2 <= 85',
        '3*x2 <= 170',
        '7*x2 <= 87',
        '8*x2 <= 87',
        '5*x1 + 2*x2 >= 15',
        '8*x0 + 5*x1 >= 22',
        '8*x0 + 5*x1 <= 75',
        '8*x0 + 2*x2 <= 61',
        '8*x0 + 5*x1 + 2*x2 <= 61',
        '8*x0 + 3*x2 <= 102',
        '8*x0 + 3*x1 <= 134',
        '8*x0 + 3*x1 + 3*x2 <= 158',
        'x1 + 7*x2 <= 35',
        '2*x0 + x1 <= 48',
        '2*x0 + x1 + 7*x2 <= 48',
        '8*x1 + 8*x2 <= 69',
        '6*x0 + 8*x2 <= 50',
        '6*x0 + 8*x1 + 8*x2 <= 84'
    ]
}
```

## 5: 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_Bobby", lb=0)
x1 = m.addVar(name="hours_worked_by_Mary", lb=0)
x2 = m.addVar(name="hours_worked_by_George", lb=0)

# Define the objective function
m.setObjective(5.96*x0 + 7.76*x1 + 5.99*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(8*x0 <= 85)
m.addConstr(8*x0 <= 170)
m.addConstr(2*x0 <= 87)
m.addConstr(6*x0 <= 87)

m.addConstr(5*x1 <= 85)
m.addConstr(3*x1 <= 170)
m.addConstr(x1 <= 87)
m.addConstr(8*x1 <= 87)

m.addConstr(2*x2 <= 85)
m.addConstr(3*x2 <= 170)
m.addConstr(7*x2 <= 87)
m.addConstr(8*x2 <= 87)

m.addConstr(5*x1 + 2*x2 >= 15)
m.addConstr(8*x0 + 5*x1 >= 22)
m.addConstr(8*x0 + 5*x1 <= 75)
m.addConstr(8*x0 + 2*x2 <= 61)
m.addConstr(8*x0 + 5*x1 + 2*x2 <= 61)
m.addConstr(8*x0 + 3*x2 <= 102)
m.addConstr(8*x0 + 3*x1 <= 134)
m.addConstr(8*x0 + 3*x1 + 3*x2 <= 158)

m.addConstr(x1 + 7*x2 <= 35)
m.addConstr(2*x0 + x1 <= 48)
m.addConstr(2*x0 + x1 + 7*x2 <= 48)

m.addConstr(8*x1 + 8*x2 <= 69)
m.addConstr(6*x0 + 8*x2 <= 50)
m.addConstr(6*x0 + 8*x1 + 8*x2 <= 84)

# Solve the model
m.optimize()

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