## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Paul', 'hours worked by George', and 'hours worked by Bobby'. Let's denote them as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $6.32x_0^2 + 6.22x_0x_1 + 6.23x_0x_2 + 5.64x_0$.

## 3: List the constraints
- $11x_0 \leq 180$ (Paul's computer competence rating constraint, but this seems to be an upper bound on $x_0$ times a constant, not directly applicable)
- $6x_0 \leq 141$ (Paul's dollar cost per hour constraint)
- $20x_1 \leq 180$ (George's computer competence rating constraint)
- $7x_1 \leq 141$ (George's dollar cost per hour constraint)
- $19x_2 \leq 180$ (Bobby's computer competence rating constraint)
- $7x_2 \leq 141$ (Bobby's dollar cost per hour constraint)
- $11x_0 + 20x_1 \geq 47$ (Combined computer competence rating constraint for Paul and George)
- $11x_0 + 20x_1 + 19x_2 \geq 59$ (Combined computer competence rating constraint for all)
- $7x_1 + 7x_2 \geq 31$ (Combined dollar cost per hour constraint for George and Bobby)
- $6x_0 + 7x_1 \geq 23$ (Combined dollar cost per hour constraint for Paul and George)
- $11x_0 + 20x_1 \leq 169$ (Upper bound on combined computer competence rating for Paul and George)
- $11x_0 + 20x_1 + 19x_2 \leq 64$ (Upper bound on combined computer competence rating for all)
- $7x_1 + 7x_2 \leq 139$ (Upper bound on combined dollar cost per hour for George and Bobby)
- $6x_0 + 7x_2 \leq 96$ (Combined dollar cost per hour constraint for Paul and Bobby)
- $6^2x_0^2 + 7^2x_1^2 + 7^2x_2^2 \leq 107$ (Constraint on squared dollar costs)
- $6x_0 + 7x_1 + 7x_2 \leq 107$ (Constraint on total dollar cost)

## 4: Correctly interpret given resource/attributes
Given resources/attributes:
- $r_0$: computer competence rating with $x_0 = 11$, $x_1 = 20$, $x_2 = 19$ and upper bound $180$.
- $r_1$: dollar cost per hour with $x_0 = 6$, $x_1 = 7$, $x_2 = 7$ and upper bound $141$.

## 5: Formulate the problem in Gurobi
To maximize $6.32x_0^2 + 6.22x_0x_1 + 6.23x_0x_2 + 5.64x_0$, we minimize $-6.32x_0^2 - 6.22x_0x_1 - 6.23x_0x_2 - 5.64x_0$.

## 6: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=0, name="hours_worked_by_Paul")
    x1 = model.addVar(lb=0, name="hours_worked_by_George")
    x2 = model.addVar(lb=0, name="hours_worked_by_Bobby")

    # Objective function
    model.setObjective(-6.32*x0**2 - 6.22*x0*x1 - 6.23*x0*x2 - 5.64*x0, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(11*x0 <= 180)
    model.addConstr(6*x0 <= 141)
    model.addConstr(20*x1 <= 180)
    model.addConstr(7*x1 <= 141)
    model.addConstr(19*x2 <= 180)
    model.addConstr(7*x2 <= 141)
    model.addConstr(11*x0 + 20*x1 >= 47)
    model.addConstr(11*x0 + 20*x1 + 19*x2 >= 59)
    model.addConstr(7*x1 + 7*x2 >= 31)
    model.addConstr(6*x0 + 7*x1 >= 23)
    model.addConstr(11*x0 + 20*x1 <= 169)
    model.addConstr(11*x0 + 20*x1 + 19*x2 <= 64)
    model.addConstr(7*x1 + 7*x2 <= 139)
    model.addConstr(6*x0 + 7*x2 <= 96)
    model.addConstr(6**2*x0**2 + 7**2*x1**2 + 7**2*x2**2 <= 107)
    model.addConstr(6*x0 + 7*x1 + 7*x2 <= 107)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Paul: ", x0.varValue)
        print("Hours worked by George: ", x1.varValue)
        print("Hours worked by Bobby: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```

## 7: Symbolic representation
```json
{
    'sym_variables': [('x0', 'hours worked by Paul'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Bobby')],
    'objective_function': '6.32*x0^2 + 6.22*x0*x1 + 6.23*x0*x2 + 5.64*x0',
    'constraints': [
        '11*x0 <= 180',
        '6*x0 <= 141',
        '20*x1 <= 180',
        '7*x1 <= 141',
        '19*x2 <= 180',
        '7*x2 <= 141',
        '11*x0 + 20*x1 >= 47',
        '11*x0 + 20*x1 + 19*x2 >= 59',
        '7*x1 + 7*x2 >= 31',
        '6*x0 + 7*x1 >= 23',
        '11*x0 + 20*x1 <= 169',
        '11*x0 + 20*x1 + 19*x2 <= 64',
        '7*x1 + 7*x2 <= 139',
        '6*x0 + 7*x2 <= 96',
        '36*x0^2 + 49*x1^2 + 49*x2^2 <= 107',
        '6*x0 + 7*x1 + 7*x2 <= 107'
    ]
}
```