## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Laura' and 'hours worked by John', which we can denote as $x_0$ and $x_1$ respectively.

## Step 2: Define the symbolic representation of the resources/attributes
The resources/attributes are given as:
- $r_0$: likelihood to quit index
- $r_1$: productivity rating
- $r_2$: work quality rating

With their respective values for Laura and John:
- $r_0$: Laura = 9, John = 14
- $r_1$: Laura = 21, John = 23
- $r_2$: Laura = 26, John = 16

And their upper bounds:
- $r_0$: 228
- $r_1$: 178
- $r_2$: 145

## Step 3: Formulate the objective function
The objective function to maximize is: $1.13x_0^2 + 5.24x_1^2 + 1.28x_1$

## 4: Formulate the constraints
1. Laura's likelihood to quit index: $9x_0$ (but this seems to be an attribute, not a constraint on $x_0$ directly, so we consider it as given)
2. Laura's productivity rating: $21x_0$ (similarly, this is an attribute)
3. Laura's work quality rating: $26x_0$ (attribute)
4. John's likelihood to quit index: $14x_1$ (attribute)
5. John's productivity rating: $23x_1$ (attribute)
6. John's work quality rating: $16x_1$ (attribute)

Given constraints:
- $9x_0 + 14x_1 \geq 71$
- $21x_0 + 23x_1 \geq 62$
- $26x_0^2 + 16x_1^2 \geq 66$
- $3x_0 - 7x_1 \geq 0$
- $9x_0 + 14x_1 \leq 198$
- $21x_0 + 23x_1 \leq 168$
- $26x_0^2 + 16x_1^2 \leq 121$ is not valid since it contradicts the $\geq 66$ and $\leq 121$ for work quality, we keep $\geq 66$ and add $\leq 121$
- $x_0$ is continuous, $x_1$ is integer.

## 5: Symbolic Representation
```json
{
    'sym_variables': [('x0', 'hours worked by Laura'), ('x1', 'hours worked by John')],
    'objective_function': '1.13*x0^2 + 5.24*x1^2 + 1.28*x1',
    'constraints': [
        '9*x0 + 14*x1 >= 71',
        '21*x0 + 23*x1 >= 62',
        '26*x0^2 + 16*x1^2 >= 66',
        '3*x0 - 7*x1 >= 0',
        '9*x0 + 14*x1 <= 198',
        '21*x0 + 23*x1 <= 168',
        '26*x0^2 + 16*x1^2 <= 121'
    ]
}
```

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

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

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

    # Objective function
    model.setObjective(1.13*x0**2 + 5.24*x1**2 + 1.28*x1, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(9*x0 + 14*x1 >= 71, name="likelihood_to_quit_index_constraint")
    model.addConstr(21*x0 + 23*x1 >= 62, name="productivity_rating_constraint")
    model.addConstr(26*x0**2 + 16*x1**2 >= 66, name="work_quality_rating_constraint")
    model.addConstr(3*x0 - 7*x1 >= 0, name="hours_worked_constraint")
    model.addConstr(9*x0 + 14*x1 <= 198, name="likelihood_to_quit_index_upper_bound")
    model.addConstr(21*x0 + 23*x1 <= 168, name="productivity_rating_upper_bound")
    model.addConstr(26*x0**2 + 16*x1**2 <= 121, name="work_quality_rating_upper_bound")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Laura: {x0.varValue}")
        print(f"Hours worked by John: {x1.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.")

solve_optimization_problem()
```