## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Dale', 'hours worked by John', and 'hours worked by George', which can be represented 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 $2.25x_0^2 + 5.18x_0x_1 + 4.6x_0x_2 + 2.19x_1x_2 + 8.59x_0 + 9.2x_1 + 10.0x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $5x_0^2 + 20x_2^2 \geq 29$
- $5x_0 + 7x_1 + 20x_2 \geq 32$
- $7x_1 + 20x_2 \leq 71$
- $5x_0 + 7x_1 \leq 72$
- $5x_0 + 7x_1 + 20x_2 \leq 175$
- $16x_0 + 16x_1 \leq 179$
- $16x_0 + 16x_2 \leq 136$
- $16x_0 + 16x_1 + 16x_2 \leq 200$

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'hours worked by Dale'), ('x1', 'hours worked by John'), ('x2', 'hours worked by George')],
'objective_function': '2.25x0^2 + 5.18x0*x1 + 4.6x0*x2 + 2.19x1*x2 + 8.59x0 + 9.2x1 + 10.0x2',
'constraints': [
'5x0^2 + 20x2^2 >= 29',
'5x0 + 7x1 + 20x2 >= 32',
'7x1 + 20x2 <= 71',
'5x0 + 7x1 <= 72',
'5x0 + 7x1 + 20x2 <= 175',
'16x0 + 16x1 <= 179',
'16x0 + 16x2 <= 136',
'16x0 + 16x1 + 16x2 <= 200'
]
}
```

## Step 5: Implement the optimization problem using Gurobi
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name='hours_worked_by_Dale', lb=0)
x1 = model.addVar(name='hours_worked_by_John', lb=0)
x2 = model.addVar(name='hours_worked_by_George', lb=0)

# Define the objective function
model.setObjective(2.25*x0**2 + 5.18*x0*x1 + 4.6*x0*x2 + 2.19*x1*x2 + 8.59*x0 + 9.2*x1 + 10.0*x2, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(5*x0**2 + 20*x2**2 >= 29)
model.addConstr(5*x0 + 7*x1 + 20*x2 >= 32)
model.addConstr(7*x1 + 20*x2 <= 71)
model.addConstr(5*x0 + 7*x1 <= 72)
model.addConstr(5*x0 + 7*x1 + 20*x2 <= 175)
model.addConstr(16*x0 + 16*x1 <= 179)
model.addConstr(16*x0 + 16*x2 <= 136)
model.addConstr(16*x0 + 16*x1 + 16*x2 <= 200)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Optimal solution found.')
    print('Hours worked by Dale:', x0.varValue)
    print('Hours worked by John:', x1.varValue)
    print('Hours worked by George:', x2.varValue)
    print('Objective function value:', model.objVal)
else:
    print('No optimal solution found.')
```