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

## Step 2: Convert the given problem into a symbolic representation
The objective function to minimize is $7.68x_0^2 + 8.67x_0x_1 + 3.79x_1^2 + 6.11x_1x_2 + 6.09x_2^2 + 4.46x_0 + 3.47x_1 + 3.11x_2$.

## 3: List the constraints
The constraints given are:
- $1.95x_0 \leq 107$
- $15.65x_0 \leq 166$
- $14.78x_0 \leq 146$
- $8.5x_0 \leq 163$
- $3.2x_1 \leq 107$
- $1.68x_1 \leq 166$
- $0.75x_1 \leq 146$
- $10.83x_1 \leq 163$
- $5.58x_2 \leq 107$
- $10.13x_2 \leq 166$
- $5.11x_2 \leq 146$
- $14.06x_2 \leq 163$
- $3.2x_1 + 5.58x_2 \geq 26$
- $1.95x_0 + 3.2x_1 + 5.58x_2 \geq 26$
- $15.65x_0^2 + 10.13x_2^2 \geq 33$
- $15.65x_0 + 1.68x_1 \geq 34$
- $15.65x_0 + 1.68x_1 + 10.13x_2 \geq 34$
- $14.78x_0 + 0.75x_1 \geq 33$
- $0.75x_1 + 5.11x_2 \geq 32$
- $14.78x_0 + 0.75x_1 + 5.11x_2 \geq 32$
- $8.5x_0 + 14.06x_2 \geq 25$
- $10.83x_1 + 14.06x_2 \geq 29$
- $8.5x_0 + 10.83x_1 + 14.06x_2 \geq 29$
- $10x_1 - 7x_2 \geq 0$
- $9x_0 - 9x_1 \geq 0$
- $1.95x_0 + 3.2x_1 \leq 36$
- $1.68x_1 + 10.13x_2 \leq 119$
- $8.5x_0^2 + 10.83x_1^2 \leq 71$
- $8.5x_0 + 10.83x_1 + 14.06x_2 \leq 162$
- $x_0$ is an integer
- $x_1$ is a continuous variable
- $x_2$ is a continuous variable

## 4: Create the symbolic representation dictionary
```json
{
    'sym_variables': [
        ('x0', 'hours worked by George'), 
        ('x1', 'hours worked by Bill'), 
        ('x2', 'hours worked by John')
    ], 
    'objective_function': '7.68*x0^2 + 8.67*x0*x1 + 3.79*x1^2 + 6.11*x1*x2 + 6.09*x2^2 + 4.46*x0 + 3.47*x1 + 3.11*x2', 
    'constraints': [
        '1.95*x0 <= 107',
        '15.65*x0 <= 166',
        '14.78*x0 <= 146',
        '8.5*x0 <= 163',
        '3.2*x1 <= 107',
        '1.68*x1 <= 166',
        '0.75*x1 <= 146',
        '10.83*x1 <= 163',
        '5.58*x2 <= 107',
        '10.13*x2 <= 166',
        '5.11*x2 <= 146',
        '14.06*x2 <= 163',
        '3.2*x1 + 5.58*x2 >= 26',
        '1.95*x0 + 3.2*x1 + 5.58*x2 >= 26',
        '15.65*x0^2 + 10.13*x2^2 >= 33',
        '15.65*x0 + 1.68*x1 >= 34',
        '15.65*x0 + 1.68*x1 + 10.13*x2 >= 34',
        '14.78*x0 + 0.75*x1 >= 33',
        '0.75*x1 + 5.11*x2 >= 32',
        '14.78*x0 + 0.75*x1 + 5.11*x2 >= 32',
        '8.5*x0 + 14.06*x2 >= 25',
        '10.83*x1 + 14.06*x2 >= 29',
        '8.5*x0 + 10.83*x1 + 14.06*x2 >= 29',
        '10*x1 - 7*x2 >= 0',
        '9*x0 - 9*x1 >= 0',
        '1.95*x0 + 3.2*x1 <= 36',
        '1.68*x1 + 10.13*x2 <= 119',
        '8.5*x0^2 + 10.83*x1^2 <= 71',
        '8.5*x0 + 10.83*x1 + 14.06*x2 <= 162'
    ]
}
```

## 5: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # hours worked by George
    x1 = model.addVar(name="x1")  # hours worked by Bill
    x2 = model.addVar(name="x2")  # hours worked by John

    # Objective function
    model.setObjective(7.68 * x0**2 + 8.67 * x0 * x1 + 3.79 * x1**2 + 6.11 * x1 * x2 + 6.09 * x2**2 + 4.46 * x0 + 3.47 * x1 + 3.11 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(1.95 * x0 <= 107)
    model.addConstr(15.65 * x0 <= 166)
    model.addConstr(14.78 * x0 <= 146)
    model.addConstr(8.5 * x0 <= 163)
    model.addConstr(3.2 * x1 <= 107)
    model.addConstr(1.68 * x1 <= 166)
    model.addConstr(0.75 * x1 <= 146)
    model.addConstr(10.83 * x1 <= 163)
    model.addConstr(5.58 * x2 <= 107)
    model.addConstr(10.13 * x2 <= 166)
    model.addConstr(5.11 * x2 <= 146)
    model.addConstr(14.06 * x2 <= 163)
    model.addConstr(3.2 * x1 + 5.58 * x2 >= 26)
    model.addConstr(1.95 * x0 + 3.2 * x1 + 5.58 * x2 >= 26)
    model.addConstr(15.65 * x0**2 + 10.13 * x2**2 >= 33)
    model.addConstr(15.65 * x0 + 1.68 * x1 >= 34)
    model.addConstr(15.65 * x0 + 1.68 * x1 + 10.13 * x2 >= 34)
    model.addConstr(14.78 * x0 + 0.75 * x1 >= 33)
    model.addConstr(0.75 * x1 + 5.11 * x2 >= 32)
    model.addConstr(14.78 * x0 + 0.75 * x1 + 5.11 * x2 >= 32)
    model.addConstr(8.5 * x0 + 14.06 * x2 >= 25)
    model.addConstr(10.83 * x1 + 14.06 * x2 >= 29)
    model.addConstr(8.5 * x0 + 10.83 * x1 + 14.06 * x2 >= 29)
    model.addConstr(10 * x1 - 7 * x2 >= 0)
    model.addConstr(9 * x0 - 9 * x1 >= 0)
    model.addConstr(1.95 * x0 + 3.2 * x1 <= 36)
    model.addConstr(1.68 * x1 + 10.13 * x2 <= 119)
    model.addConstr(8.5 * x0**2 + 10.83 * x1**2 <= 71)
    model.addConstr(8.5 * x0 + 10.83 * x1 + 14.06 * x2 <= 162)

    # Solve the model
    model.optimize()

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

solve_optimization_problem()
```