## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bill', 'hours worked by Peggy', and 'hours worked by Hank', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the given attributes into a usable format
The given attributes are:
- $r_0$: productivity rating
- $r_1$: computer competence rating
- $r_2$: work quality rating
- $r_3$: dollar cost per hour
- $r_4$: likelihood to quit index

With their respective values for Bill, Peggy, and Hank:
- $r_0 = [0.46, 6.72, 10.12]$
- $r_1 = [1.82, 2.03, 5.95]$
- $r_2 = [6.95, 1.29, 12.71]$
- $r_3 = [8.81, 1.9, 9.2]$
- $r_4 = [4.17, 10.11, 0.97]$

## 3: Express the objective function in symbolic notation
The objective function to minimize is: $1x_1^2 + 9x_1x_2 + 8x_2^2 + 1x_2x_3 + 7x_2 + 7x_3$.

## 4: List all constraints in symbolic notation
Constraints:
1. $0.46x_1 \leq 144$
2. $1.82x_1 \leq 116$
3. $6.95x_1 \leq 152$
4. $8.81x_1 \leq 76$
5. $4.17x_1 \leq 99$
6. $6.72x_2 \leq 144$
7. $2.03x_2 \leq 116$
8. $1.29x_2 \leq 152$
9. $1.9x_2 \leq 76$
10. $10.11x_2 \leq 99$
11. $10.12x_3 \leq 144$
12. $5.95x_3 \leq 116$
13. $12.71x_3 \leq 152$
14. $9.2x_3 \leq 76$
15. $0.97x_3 \leq 99$
16. $0.46x_1^2 + 10.12x_3^2 \geq 39$
17. $6.72x_2 + 10.12x_3 \geq 18$
18. $0.46x_1 + 6.72x_2 + 10.12x_3 \geq 18$
19. $1.82x_1 + 2.03x_2 \geq 16$
20. $2.03x_2 + 5.95x_3 \geq 36$
21. $1.82x_1 + 2.03x_2 + 5.95x_3 \geq 34$
22. $6.95x_1 + 12.71x_3 \geq 31$
23. $6.95x_1 + 1.29x_2 \geq 47$
24. $6.95x_1 + 1.29x_2 + 12.71x_3 \geq 47$
25. $8.81x_1^2 + 9.2x_3^2 \geq 11$
26. $8.81x_1 + 1.9x_2 \geq 14$
27. $8.81x_1 + 1.9x_2 + 9.2x_3 \geq 14$
28. $4.17x_1 + 10.11x_2 \geq 31$
29. $10.11x_2^2 + 0.97x_3^2 \geq 30$
30. $4.17x_1 + 10.11x_2 + 0.97x_3 \geq 30$
31. $5x_2 - 5x_3 \geq 0$
32. $2.03x_2 + 5.95x_3 \leq 88$
33. $1.82x_1^2 + 2.03x_2^2 \leq 54$
34. $4.17x_1 + 10.11x_2 \leq 62$
35. $4.17x_1^2 + 10.11x_2^2 + 0.97x_3^2 \leq 96$

## 5: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Bill'),
        ('x2', 'hours worked by Peggy'),
        ('x3', 'hours worked by Hank')
    ],
    'objective_function': '1*x1^2 + 9*x1*x2 + 8*x2^2 + 1*x2*x3 + 7*x2 + 7*x3',
    'constraints': [
        '0.46*x1 <= 144',
        '1.82*x1 <= 116',
        '6.95*x1 <= 152',
        '8.81*x1 <= 76',
        '4.17*x1 <= 99',
        '6.72*x2 <= 144',
        '2.03*x2 <= 116',
        '1.29*x2 <= 152',
        '1.9*x2 <= 76',
        '10.11*x2 <= 99',
        '10.12*x3 <= 144',
        '5.95*x3 <= 116',
        '12.71*x3 <= 152',
        '9.2*x3 <= 76',
        '0.97*x3 <= 99',
        '0.46*x1^2 + 10.12*x3^2 >= 39',
        '6.72*x2 + 10.12*x3 >= 18',
        '0.46*x1 + 6.72*x2 + 10.12*x3 >= 18',
        '1.82*x1 + 2.03*x2 >= 16',
        '2.03*x2 + 5.95*x3 >= 36',
        '1.82*x1 + 2.03*x2 + 5.95*x3 >= 34',
        '6.95*x1 + 12.71*x3 >= 31',
        '6.95*x1 + 1.29*x2 >= 47',
        '6.95*x1 + 1.29*x2 + 12.71*x3 >= 47',
        '8.81*x1^2 + 9.2*x3^2 >= 11',
        '8.81*x1 + 1.9*x2 >= 14',
        '8.81*x1 + 1.9*x2 + 9.2*x3 >= 14',
        '4.17*x1 + 10.11*x2 >= 31',
        '10.11*x2^2 + 0.97*x3^2 >= 30',
        '4.17*x1 + 10.11*x2 + 0.97*x3 >= 30',
        '5*x2 - 5*x3 >= 0',
        '2.03*x2 + 5.95*x3 <= 88',
        '1.82*x1^2 + 2.03*x2^2 <= 54',
        '4.17*x1 + 10.11*x2 <= 62',
        '4.17*x1^2 + 10.11*x2^2 + 0.97*x3^2 <= 96'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="x1", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = m.addVar(name="x2", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x3 = m.addVar(name="x3", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Objective function
m.setObjective(1 * x1**2 + 9 * x1 * x2 + 8 * x2**2 + 1 * x2 * x3 + 7 * x2 + 7 * x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(0.46 * x1 <= 144)
m.addConstr(1.82 * x1 <= 116)
m.addConstr(6.95 * x1 <= 152)
m.addConstr(8.81 * x1 <= 76)
m.addConstr(4.17 * x1 <= 99)
m.addConstr(6.72 * x2 <= 144)
m.addConstr(2.03 * x2 <= 116)
m.addConstr(1.29 * x2 <= 152)
m.addConstr(1.9 * x2 <= 76)
m.addConstr(10.11 * x2 <= 99)
m.addConstr(10.12 * x3 <= 144)
m.addConstr(5.95 * x3 <= 116)
m.addConstr(12.71 * x3 <= 152)
m.addConstr(9.2 * x3 <= 76)
m.addConstr(0.97 * x3 <= 99)
m.addConstr(0.46 * x1**2 + 10.12 * x3**2 >= 39)
m.addConstr(6.72 * x2 + 10.12 * x3 >= 18)
m.addConstr(0.46 * x1 + 6.72 * x2 + 10.12 * x3 >= 18)
m.addConstr(1.82 * x1 + 2.03 * x2 >= 16)
m.addConstr(2.03 * x2 + 5.95 * x3 >= 36)
m.addConstr(1.82 * x1 + 2.03 * x2 + 5.95 * x3 >= 34)
m.addConstr(6.95 * x1 + 12.71 * x3 >= 31)
m.addConstr(6.95 * x1 + 1.29 * x2 >= 47)
m.addConstr(6.95 * x1 + 1.29 * x2 + 12.71 * x3 >= 47)
m.addConstr(8.81 * x1**2 + 9.2 * x3**2 >= 11)
m.addConstr(8.81 * x1 + 1.9 * x2 >= 14)
m.addConstr(8.81 * x1 + 1.9 * x2 + 9.2 * x3 >= 14)
m.addConstr(4.17 * x1 + 10.11 * x2 >= 31)
m.addConstr(10.11 * x2**2 + 0.97 * x3**2 >= 30)
m.addConstr(4.17 * x1 + 10.11 * x2 + 0.97 * x3 >= 30)
m.addConstr(5 * x2 - 5 * x3 >= 0)
m.addConstr(2.03 * x2 + 5.95 * x3 <= 88)
m.addConstr(1.82 * x1**2 + 2.03 * x2**2 <= 54)
m.addConstr(4.17 * x1 + 10.11 * x2 <= 62)
m.addConstr(4.17 * x1**2 + 10.11 * x2**2 + 0.97 * x3**2 <= 96)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```