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

## Step 2: Convert the given resources/attributes into a usable form
The resources/attributes given are:
- $r_0$: {'description': 'productivity rating', 'upper_bound': 197, 'x0': 7, 'x1': 1, 'x2': 17}
- $r_1$: {'description': 'paperwork competence rating', 'upper_bound': 199, 'x0': 16, 'x1': 10, 'x2': 5}

## 3: Define the objective function in symbolic notation
The objective function to minimize is $6.28x_0^2 + 4.64x_2^2 + 2.73x_0$.

## 4: List all the constraints in symbolic notation
The constraints are:
1. $x_0 \geq 0$ (Implicit, as hours cannot be negative)
2. $x_1 \geq 0$ (Implicit, as hours cannot be negative)
3. $x_2 \geq 0$ (Implicit, as hours cannot be negative)
4. $x_0^2 \cdot 7^2 + x_1^2 \cdot 1^2 + x_2^2 \cdot 17^2 \geq 0$ is not directly given, instead we have:
5. $x_1^2 + x_2^2 \geq 42$ (productivity rating constraint)
6. $7x_0 + x_1 + 17x_2 \geq 42$ (total combined productivity rating)
7. $16x_0 + 10x_1 \geq 49$ (total combined paperwork competence rating from Jean and George)
8. $16x_0 + 10x_1 + 5x_2 \geq 49$ (total combined paperwork competence rating from all)
9. $-4x_0 + 10x_1 \geq 0$ (specific constraint)
10. $16x_0 + 5x_2 \leq 125$ (paperwork competence rating from Jean and Dale)
11. $10x_1 + 5x_2 \leq 143$ (paperwork competence rating from George and Dale)

## 5: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'hours worked by Jean'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Dale')],
'objective_function': '6.28*x0^2 + 4.64*x2^2 + 2.73*x0',
'constraints': [
'x0 >= 0', 'x1 >= 0', 'x2 >= 0',
'x1^2 + x2^2 >= 42',
'7*x0 + x1 + 17*x2 >= 42',
'16*x0 + 10*x1 >= 49',
'16*x0 + 10*x1 + 5*x2 >= 49',
'-4*x0 + 10*x1 >= 0',
'16*x0 + 5*x2 <= 125',
'10*x1 + 5*x2 <= 143'
]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Jean
    x1 = model.addVar(name="x1", lb=0)  # hours worked by George
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Dale

    # Define the objective function
    model.setObjective(6.28 * x0**2 + 4.64 * x2**2 + 2.73 * x0, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(x1**2 + x2**2 >= 42)
    model.addConstr(7 * x0 + x1 + 17 * x2 >= 42)
    model.addConstr(16 * x0 + 10 * x1 >= 49)
    model.addConstr(16 * x0 + 10 * x1 + 5 * x2 >= 49)
    model.addConstr(-4 * x0 + 10 * x1 >= 0)
    model.addConstr(16 * x0 + 5 * x2 <= 125)
    model.addConstr(10 * x1 + 5 * x2 <= 143)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Hours worked by Jean: ", x0.varValue)
        print("Hours worked by George: ", x1.varValue)
        print("Hours worked by Dale: ", x2.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```