## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Ringo', 'hours worked by Jean', and 'hours worked by George', 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: $1 \cdot x_0^2 + 4 \cdot x_0 \cdot x_1 + 2 \cdot x_0 \cdot x_2 + 6 \cdot x_1^2 + 1 \cdot x_1 \cdot x_2 + 9 \cdot x_2^2 + 4 \cdot x_0 + 7 \cdot x_1 + 4 \cdot x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $5x_0 = 5$ (Ringo's computer competence rating)
- $6x_0 = 6$ (Ringo's dollar cost per hour)
- $2x_1 = 2$ (Jean's computer competence rating)
- $9x_1 = 9$ (Jean's dollar cost per hour)
- $7x_2 = 7$ (George's computer competence rating)
- $1x_2 = 1$ (George's dollar cost per hour)
- $5x_0 + 2x_1 \geq 24$ (total combined computer competence rating from hours worked by Ringo and Jean)
- $5^2x_0^2 + 7^2x_2^2 \geq 42$ (total combined computer competence rating from hours worked by Ringo squared and George squared)
- $2^2x_1^2 + 7^2x_2^2 \geq 38$ (total combined computer competence rating from hours worked by Jean squared and George squared)
- $6^2x_0^2 + 9^2x_1^2 + 1^2x_2^2 \geq 19$ (total combined dollar cost per hour from hours worked by Ringo squared, Jean squared, and George squared)
- $5^2x_0^2 + 2^2x_1^2 \leq 42$ (total combined computer competence rating from hours worked by Ringo squared and Jean squared)
- $2^2x_1^2 + 7^2x_2^2 \leq 124$ (total combined computer competence rating from hours worked by Jean squared and George squared)
- $5x_0 + 2x_1 + 7x_2 \leq 124$ (total combined computer competence rating from hours worked by Ringo, Jean, and George)
- $9x_1 + 1x_2 \leq 47$ (total combined dollar cost per hour from hours worked by Jean and George)
- $6^2x_0^2 + 1^2x_2^2 \leq 93$ (total combined dollar cost per hour from hours worked by Ringo squared and George squared)
- $6x_0 + 9x_1 \leq 33$ (total combined dollar cost per hour from hours worked by Ringo and Jean)
- $6^2x_0^2 + 9^2x_1^2 + 1^2x_2^2 \leq 84$ (total combined dollar cost per hour from hours worked by Ringo squared, Jean squared, and George squared)
- $6x_0 + 9x_1 + 1x_2 \leq 84$ (total combined dollar cost per hour from hours worked by Ringo, Jean, and George)

## 4: Correct the understanding of the constraints
Upon closer inspection, the first six constraints seem to be more about defining the parameters rather than limiting the variables $x_0$, $x_1$, and $x_2$. The actual constraints that limit $x_0$, $x_1$, and $x_2$ are the inequalities and equalities provided afterwards.

## 5: Formulate the problem in Gurobi
To maximize $1x_0^2 + 4x_0x_1 + 2x_0x_2 + 6x_1^2 + 1x_1x_2 + 9x_2^2 + 4x_0 + 7x_1 + 4x_2$ subject to the given constraints, we use Gurobi's Python interface.

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

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

# Define the variables
x0 = m.addVar(name="x0", integer=True)  # hours worked by Ringo
x1 = m.addVar(name="x1", integer=True)  # hours worked by Jean
x2 = m.addVar(name="x2")  # hours worked by George

# Objective function
m.setObjective(1*x0**2 + 4*x0*x1 + 2*x0*x2 + 6*x1**2 + 1*x1*x2 + 9*x2**2 + 4*x0 + 7*x1 + 4*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(5*x0 == 5, name="Ringo_computer")
m.addConstr(6*x0 == 6, name="Ringo_cost")
m.addConstr(2*x1 == 2, name="Jean_computer")
m.addConstr(9*x1 == 9, name="Jean_cost")
m.addConstr(7*x2 == 7, name="George_computer")
m.addConstr(1*x2 == 1, name="George_cost")

m.addConstr(5*x0 + 2*x1 >= 24, name="min_computer_rating_Ringo_Jean")
m.addConstr(25*x0**2 + 49*x2**2 >= 42, name="min_computer_rating_Ringo_George")
m.addConstr(4*x1**2 + 49*x2**2 >= 38, name="min_computer_rating_Jean_George")
m.addConstr(36*x0**2 + 81*x1**2 + x2**2 >= 19, name="min_dollar_cost")
m.addConstr(25*x0**2 + 4*x1**2 <= 42, name="max_computer_rating_Ringo_Jean")
m.addConstr(4*x1**2 + 49*x2**2 <= 124, name="max_computer_rating_Jean_George")
m.addConstr(5*x0 + 2*x1 + 7*x2 <= 124, name="max_total_computer_rating")
m.addConstr(9*x1 + x2 <= 47, name="max_dollar_cost_Jean_George")
m.addConstr(36*x0**2 + x2**2 <= 93, name="max_dollar_cost_Ringo_George")
m.addConstr(6*x0 + 9*x1 <= 33, name="max_dollar_cost_Ringo_Jean")
m.addConstr(36*x0**2 + 81*x1**2 + x2**2 <= 84, name="max_dollar_cost_all")
m.addConstr(6*x0 + 9*x1 + x2 <= 84, name="max_total_dollar_cost")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic Representation
```json
{
    'sym_variables': [('x0', 'hours worked by Ringo'), ('x1', 'hours worked by Jean'), ('x2', 'hours worked by George')],
    'objective_function': '1*x0^2 + 4*x0*x1 + 2*x0*x2 + 6*x1^2 + 1*x1*x2 + 9*x2^2 + 4*x0 + 7*x1 + 4*x2',
    'constraints': [
        '5*x0 = 5',
        '6*x0 = 6',
        '2*x1 = 2',
        '9*x1 = 9',
        '7*x2 = 7',
        '1*x2 = 1',
        '5*x0 + 2*x1 >= 24',
        '25*x0^2 + 49*x2^2 >= 42',
        '4*x1^2 + 49*x2^2 >= 38',
        '36*x0^2 + 81*x1^2 + x2^2 >= 19',
        '25*x0^2 + 4*x1^2 <= 42',
        '4*x1^2 + 49*x2^2 <= 124',
        '5*x0 + 2*x1 + 7*x2 <= 124',
        '9*x1 + x2 <= 47',
        '36*x0^2 + x2^2 <= 93',
        '6*x0 + 9*x1 <= 33',
        '36*x0^2 + 81*x1^2 + x2^2 <= 84',
        '6*x0 + 9*x1 + x2 <= 84'
    ]
}
```