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

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $7.22x_1^2 + 3.77x_1x_2 + 7.44x_1 + 1.6x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $16x_1 + 1x_2 \geq 37$ (total combined organization score from hours worked by George, and hours worked by Bill has to be 37 or more, but first we need to establish the correct formulation based on given resources)
- $14x_1 + 17x_2 \geq 25$ (total combined productivity rating from hours worked by George, and hours worked by Bill should be 25 at a minimum)
- $-x_1^2 + x_2^2 \geq 0$
- $16^2x_1^2 + 1^2x_2^2 \leq 79$ (total combined organization score from hours worked by George squared, and hours worked by Bill squared has to be at maximum 79, but correctly it should consider $x_0$ and $x_1$ for organization score)
- Correcting based on resource attributes: 
  - Organization score constraint: $16x_1 + 1x_2 \geq 37$
  - Productivity rating constraint: $14x_1 + 17x_2 \geq 25$
  - The correct formulation for organization score squared and productivity rating should directly utilize $x_1$ and $x_2$ in constraints.

## 4: Correctly formulate constraints based on problem description
Given resources/attributes:
- $r0$: organization score, with $x_0 = 16$, $x_1 = 1$
- $r1$: productivity rating, with $x0 = 14$, $x1 = 17$

## 5: Establish correct constraints
- Organization score: $16x_1 + x_2 \geq 37$
- Productivity rating: $14x_1 + 17x_2 \geq 25$
- $-x_1^2 + x_2^2 \geq 0$
- $(16x_1)^2 + (x_2)^2 \leq 79$ 
- $16x_1 + x_2 \leq 79$
- $14x_1 + 17x_2 \leq 81$

## 6: Symbolic Representation
```json
{
'sym_variables': [('x1', 'hours worked by George'), ('x2', 'hours worked by Bill')],
'objective_function': '7.22*x1^2 + 3.77*x1*x2 + 7.44*x1 + 1.6*x2',
'constraints': [
    '16*x1 + 1*x2 >= 37',
    '14*x1 + 17*x2 >= 25',
    '-x1^2 + x2^2 >= 0',
    '(16*x1)^2 + (1*x2)^2 <= 79',
    '16*x1 + 1*x2 <= 79',
    '14*x1 + 17*x2 <= 81'
]
}
```

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

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

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

    # Objective function
    model.setObjective(7.22*x1**2 + 3.77*x1*x2 + 7.44*x1 + 1.6*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(16*x1 + x2 >= 37, name="organization_score_constraint")
    model.addConstr(14*x1 + 17*x2 >= 25, name="productivity_rating_constraint")
    model.addConstr(-x1**2 + x2**2 >= 0, name="hours_worked_constraint")
    model.addConstr((16*x1)**2 + (x2)**2 <= 79, name="organization_score_squared_constraint")
    model.addConstr(16*x1 + x2 <= 79, name="total_organization_score_constraint")
    model.addConstr(14*x1 + 17*x2 <= 81, name="total_productivity_rating_constraint")

    # Optimize
    model.optimize()

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

optimization_problem()
```