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

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $8.79x_0^2 + 8.32x_0x_1 + 3.36x_1^2 + 1.92x_1x_2 + 7.38x_2^2 + 7.99x_0 + 4.63x_1 + 6.45x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $4.53x_0 \leq 128$ (work quality rating for Ringo)
- $1.66x_0 \leq 141$ (computer competence rating for Ringo)
- $10.63x_1 \leq 128$ (work quality rating for Bobby)
- $6.57x_1 \leq 141$ (computer competence rating for Bobby)
- $11.55x_2 \leq 128$ (work quality rating for Jean)
- $11.7x_2 \leq 141$ (computer competence rating for Jean)
- $4.53x_0^2 + 10.63x_1^2 \geq 28$ (combined work quality rating)
- $4.53x_0 + 11.55x_2 \geq 28$ (combined work quality rating)
- $1.66x_0 + 11.7x_2 \geq 33$ (combined computer competence rating)
- $1.66x_0^2 + 6.57x_1^2 + 11.7x_2^2 \geq 40$ (combined computer competence rating)
- $10.63x_1 + 11.55x_2 \leq 60$ (combined work quality rating)
- $4.53x_0^2 + 11.55x_2^2 \leq 87$ (combined work quality rating)
- $4.53x_0 + 10.63x_1 + 11.55x_2 \leq 87$ (combined work quality rating)
- $1.66x_0^2 + 6.57x_1^2 \leq 119$ (combined computer competence rating)
- $1.66x_0 + 11.7x_2 \leq 137$ (combined computer competence rating)
- $1.66x_0 + 6.57x_1 + 11.7x_2 \leq 70$ (combined computer competence rating)

## 4: Specify variable bounds
- $x_0$ is continuous
- $x_1$ is integer
- $x_2$ is integer

## 5: Create the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by Ringo'), ('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Jean')],
    'objective_function': '8.79*x0^2 + 8.32*x0*x1 + 3.36*x1^2 + 1.92*x1*x2 + 7.38*x2^2 + 7.99*x0 + 4.63*x1 + 6.45*x2',
    'constraints': [
        '4.53*x0 <= 128',
        '1.66*x0 <= 141',
        '10.63*x1 <= 128',
        '6.57*x1 <= 141',
        '11.55*x2 <= 128',
        '11.7*x2 <= 141',
        '4.53*x0^2 + 10.63*x1^2 >= 28',
        '4.53*x0 + 11.55*x2 >= 28',
        '1.66*x0 + 11.7*x2 >= 33',
        '1.66*x0^2 + 6.57*x1^2 + 11.7*x2^2 >= 40',
        '10.63*x1 + 11.55*x2 <= 60',
        '4.53*x0^2 + 11.55*x2^2 <= 87',
        '4.53*x0 + 10.63*x1 + 11.55*x2 <= 87',
        '1.66*x0^2 + 6.57*x1^2 <= 119',
        '1.66*x0 + 11.7*x2 <= 137',
        '1.66*x0 + 6.57*x1 + 11.7*x2 <= 70'
    ]
}
```

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

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

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0")
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x2", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(8.79*x0**2 + 8.32*x0*x1 + 3.36*x1**2 + 1.92*x1*x2 + 7.38*x2**2 + 7.99*x0 + 4.63*x1 + 6.45*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(4.53*x0 <= 128)
    model.addConstr(1.66*x0 <= 141)
    model.addConstr(10.63*x1 <= 128)
    model.addConstr(6.57*x1 <= 141)
    model.addConstr(11.55*x2 <= 128)
    model.addConstr(11.7*x2 <= 141)
    model.addConstr(4.53*x0**2 + 10.63*x1**2 >= 28)
    model.addConstr(4.53*x0 + 11.55*x2 >= 28)
    model.addConstr(1.66*x0 + 11.7*x2 >= 33)
    model.addConstr(1.66*x0**2 + 6.57*x1**2 + 11.7*x2**2 >= 40)
    model.addConstr(10.63*x1 + 11.55*x2 <= 60)
    model.addConstr(4.53*x0**2 + 11.55*x2**2 <= 87)
    model.addConstr(4.53*x0 + 10.63*x1 + 11.55*x2 <= 87)
    model.addConstr(1.66*x0**2 + 6.57*x1**2 <= 119)
    model.addConstr(1.66*x0 + 11.7*x2 <= 137)
    model.addConstr(1.66*x0 + 6.57*x1 + 11.7*x2 <= 70)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
    else:
        print("No solution found")

optimize_problem()
```