## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bobby', 'hours worked by Dale', and 'hours worked by Jean', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the given attributes into a usable format
The given attributes are:
- $r_0$: work quality rating with $x_0 = 17$, $x_1 = 20$, $x_2 = 11$, and upper bound $140$
- $r_1$: productivity rating with $x_0 = 18$, $x_1 = 2$, $x_2 = 17$, and upper bound $112$
- $r_2$: paperwork competence rating with $x_0 = 14$, $x_1 = 1$, $x_2 = 16$, and upper bound $84$
- $r_3$: computer competence rating with $x_0 = 6$, $x_1 = 3$, $x_2 = 1$, and upper bound $95$
- $r_4$: organization score with $x_0 = 8$, $x_1 = 6$, $x_2 = 19$, and upper bound $195$

## 3: Express the objective function in symbolic notation
The objective function to minimize is $7.57x_0^2 + 9.82x_0x_1 + 9.01x_0x_2 + 7.66x_1^2 + 1.58x_1x_2 + 9.11x_2^2 + 9.12x_0$.

## 4: List the constraints in symbolic notation
Constraints:
1. $17x_0 \leq 140$
2. $18x_0 \leq 112$
3. $14x_0 \leq 84$
4. $6x_0 \leq 95$
5. $8x_0 \leq 195$
6. $20x_1 \leq 140$
7. $2x_1 \leq 112$
8. $1x_1 \leq 84$
9. $3x_1 \leq 95$
10. $6x_1 \leq 195$
11. $11x_2 \leq 140$
12. $17x_2 \leq 112$
13. $16x_2 \leq 84$
14. $1x_2 \leq 95$
15. $19x_2 \leq 195$
16. $17x_0 + 20x_1 \geq 36$
17. $20x_1 + 11x_2 \geq 28$
18. $17x_0 + 20x_1 + 11x_2 \geq 28$
19. $2x_1 + 17x_2 \geq 27$
20. $18x_0 + 2x_1 + 17x_2 \geq 27$
21. $14x_0 + 16x_2 \geq 10$
22. $1x_1^2 + 16x_2^2 \geq 13$
23. $14x_0 + 1x_1 \geq 10$
24. $14x_0 + 1x_1 + 16x_2 \geq 10$
25. $6x_0 + 1x_2 \geq 24$
26. $6^2x_0^2 + 3^2x_1^2 \geq 16$
27. $6x_0 + 3x_1 + 1x_2 \geq 29$
28. $6x_0 + 3x_1 + 1x_2 \geq 29$
29. $8x_0^2 + 19x_2^2 \geq 49$
30. $8x_0 + 6x_1 \geq 40$
31. $8x_0 + 6x_1 + 19x_2 \geq 40$
32. $-5x_0 + 6x_1 \geq 0$
33. $18^2x_0^2 + 17^2x_2^2 \leq 98$
34. $2x_1 + 17x_2 \leq 106$
35. $18x_0 + 2x_1 \leq 110$

## 5: Symbolic representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bobby'),
        ('x1', 'hours worked by Dale'),
        ('x2', 'hours worked by Jean')
    ],
    'objective_function': '7.57x0^2 + 9.82x0*x1 + 9.01x0*x2 + 7.66x1^2 + 1.58x1*x2 + 9.11x2^2 + 9.12x0',
    'constraints': [
        '17*x0 <= 140',
        '18*x0 <= 112',
        '14*x0 <= 84',
        '6*x0 <= 95',
        '8*x0 <= 195',
        '20*x1 <= 140',
        '2*x1 <= 112',
        '1*x1 <= 84',
        '3*x1 <= 95',
        '6*x1 <= 195',
        '11*x2 <= 140',
        '17*x2 <= 112',
        '16*x2 <= 84',
        '1*x2 <= 95',
        '19*x2 <= 195',
        '17*x0 + 20*x1 >= 36',
        '20*x1 + 11*x2 >= 28',
        '17*x0 + 20*x1 + 11*x2 >= 28',
        '2*x1 + 17*x2 >= 27',
        '18*x0 + 2*x1 + 17*x2 >= 27',
        '14*x0 + 16*x2 >= 10',
        'x1^2 + 16*x2^2 >= 13',
        '14*x0 + x1 >= 10',
        '14*x0 + x1 + 16*x2 >= 10',
        '6*x0 + x2 >= 24',
        '36*x0^2 + 9*x1^2 >= 16',
        '6*x0 + 3*x1 + x2 >= 29',
        '6*x0 + 3*x1 + x2 >= 29',
        '8*x0^2 + 19*x2^2 >= 49',
        '8*x0 + 6*x1 >= 40',
        '8*x0 + 6*x1 + 19*x2 >= 40',
        '-5*x0 + 6*x1 >= 0',
        '324*x0^2 + 289*x2^2 <= 98',
        '2*x1 + 17*x2 <= 106',
        '18*x0 + 2*x1 <= 110'
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

def optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Bobby
    x1 = model.addVar(name="x1", lb=0, integrality=1)  # hours worked by Dale
    x2 = model.addVar(name="x2", lb=0, integrality=1)  # hours worked by Jean

    # Objective function
    model.setObjective(7.57 * x0**2 + 9.82 * x0 * x1 + 9.01 * x0 * x2 + 7.66 * x1**2 + 1.58 * x1 * x2 + 9.11 * x2**2 + 9.12 * x0, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(17 * x0 <= 140)
    model.addConstr(18 * x0 <= 112)
    model.addConstr(14 * x0 <= 84)
    model.addConstr(6 * x0 <= 95)
    model.addConstr(8 * x0 <= 195)
    model.addConstr(20 * x1 <= 140)
    model.addConstr(2 * x1 <= 112)
    model.addConstr(x1 <= 84)
    model.addConstr(3 * x1 <= 95)
    model.addConstr(6 * x1 <= 195)
    model.addConstr(11 * x2 <= 140)
    model.addConstr(17 * x2 <= 112)
    model.addConstr(16 * x2 <= 84)
    model.addConstr(x2 <= 95)
    model.addConstr(19 * x2 <= 195)
    model.addConstr(17 * x0 + 20 * x1 >= 36)
    model.addConstr(20 * x1 + 11 * x2 >= 28)
    model.addConstr(17 * x0 + 20 * x1 + 11 * x2 >= 28)
    model.addConstr(2 * x1 + 17 * x2 >= 27)
    model.addConstr(18 * x0 + 2 * x1 + 17 * x2 >= 27)
    model.addConstr(14 * x0 + 16 * x2 >= 10)
    model.addConstr(x1**2 + 16 * x2**2 >= 13)
    model.addConstr(14 * x0 + x1 >= 10)
    model.addConstr(14 * x0 + x1 + 16 * x2 >= 10)
    model.addConstr(6 * x0 + x2 >= 24)
    model.addConstr(36 * x0**2 + 9 * x1**2 >= 16)
    model.addConstr(6 * x0 + 3 * x1 + x2 >= 29)
    model.addConstr(6 * x0 + 3 * x1 + x2 >= 29)
    model.addConstr(8 * x0**2 + 19 * x2**2 >= 49)
    model.addConstr(8 * x0 + 6 * x1 >= 40)
    model.addConstr(8 * x0 + 6 * x1 + 19 * x2 >= 40)
    model.addConstr(-5 * x0 + 6 * x1 >= 0)
    model.addConstr(324 * x0**2 + 289 * x2**2 <= 98)
    model.addConstr(2 * x1 + 17 * x2 <= 106)
    model.addConstr(18 * x0 + 2 * x1 <= 110)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Bobby: {x0.varValue}")
        print(f"Hours worked by Dale: {x1.varValue}")
        print(f"Hours worked by Jean: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

optimization_problem()
```