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

## Step 2: Convert the given attributes into symbolic constraints
Given attributes:
- $r_0$: likelihood to quit index with $x_0 = 16$ for Bobby and $x_1 = 24$ for Laura, and an upper bound of 66.
- $r_1$: productivity rating with $x_0 = 1$ for Bobby and $x_1 = 21$ for Laura, and an upper bound of 218.

## 3: Formulate the objective function
The objective function to minimize is $8.42x_1^2 + 1.43x_1x_2 + 9.94x_2^2 + 5.19x_2$.

## 4: List all constraints
1. Bobby's likelihood to quit index is 16: $16x_1 \leq 66$ is not correct, it seems $16$ is a fixed value for Bobby, not a coefficient. So, we consider it as a given value, not a constraint in the traditional sense but rather $x_0 = 16$ for Bobby.
2. Bobby has a productivity rating of 1: Similarly, $1x_1$ is not a constraint but $x_0 = 1$.
3. Laura's likelihood to quit index is 24: $24x_2 \leq 66$.
4. Laura has a productivity rating of 21: $21x_2$ is not a constraint in the traditional sense.
5. The total combined likelihood to quit index from hours worked by Bobby plus hours worked by Laura has to be 29 at a minimum: $16x_1 + 24x_2 \geq 29$.
6. The total combined productivity rating from hours worked by Bobby plus hours worked by Laura should be at least 95: $1x_1 + 21x_2 \geq 95$.
7. $-1 \times$ the number of hours worked by Bobby, plus 7 times the number of hours worked by Laura should be at minimum zero: $-x_1 + 7x_2 \geq 0$.
8. The total combined likelihood to quit index from hours worked by Bobby, and hours worked by Laura has to be less than or equal to 35: $16x_1 + 24x_2 \leq 35$.
9. The total combined productivity rating from hours worked by Bobby squared, and hours worked by Laura squared must be as much or less than 124: $x_1^2 + x_2^2 \leq 124$.
10. $x_1$ must be an integer (non-fractional), $x_2$ is not restricted to integers.

## 5: Correct and Clarify Constraints
Correcting and clarifying:
- The actual constraints from given data are:
  - $16x_1 \leq 66$,
  - $1x_1 \leq 218$,
  - $24x_2 \leq 66$,
  - $21x_2 \leq 218$.

## 6: Symbolic Representation
The symbolic representation of the problem:
```json
{
    'sym_variables': [('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Laura')],
    'objective_function': '8.42*x1^2 + 1.43*x1*x2 + 9.94*x2^2 + 5.19*x2',
    'constraints': [
        '16*x1 + 24*x2 >= 29',
        '1*x1 + 21*x2 >= 95',
        '-x1 + 7*x2 >= 0',
        '16*x1 + 24*x2 <= 35',
        'x1^2 + x2^2 <= 124',
        'x1 <= 66/16',
        'x1 <= 218',
        'x2 <= 66/24',
        'x2 <= 218/21'
    ]
}
```

## 7: Gurobi Code
Now, let's write the Gurobi code for this problem:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Bobby", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="hours_worked_by_Laura")

    # Objective function
    model.setObjective(8.42 * x1**2 + 1.43 * x1 * x2 + 9.94 * x2**2 + 5.19 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(16 * x1 + 24 * x2 >= 29)
    model.addConstr(1 * x1 + 21 * x2 >= 95)
    model.addConstr(-x1 + 7 * x2 >= 0)
    model.addConstr(16 * x1 + 24 * x2 <= 35)
    model.addConstr(x1**2 + x2**2 <= 124)
    model.addConstr(x1 <= 66/16)
    model.addConstr(x1 <= 218)
    model.addConstr(x2 <= 66/24)
    model.addConstr(x2 <= 218/21)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Hours worked by Bobby: ", x1.varValue)
        print("Hours worked by Laura: ", x2.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```