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

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables and their corresponding natural language objects are:
- $x_0$ : hours worked by Laura
- $x_1$ : hours worked by George
- $x_2$ : hours worked by Paul

## 3: Define the objective function in symbolic notation
The objective function to minimize is $4x_0^2 + 8x_0x_1 + 2x_1x_2 + 2x_2^2 + 4x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $7x_0 \leq 76$
- $1x_0 \leq 82$
- $9x_0 \leq 130$
- $3x_1 \leq 76$
- $10x_1 \leq 82$
- $7x_1 \leq 130$
- $3x_2 \leq 76$
- $9x_2 \leq 82$
- $1x_2 \leq 130$
- $7x_0^2 + 3x_1^2 \geq 24$
- $7x_0 + 3x_2 \geq 23$
- $7x_0^2 + 3x_1^2 + 3x_2^2 \geq 23$
- $7x_0 + 3x_1 + 3x_2 \geq 23$
- $1x_0^2 + 10x_1^2 \geq 19$
- $10x_1 + 9x_2 \geq 26$
- $1x_0 + 10x_1 + 9x_2 \geq 26$
- $7x_1 + 1x_2 \geq 22$
- $9x_0^2 + 7x_1^2 \geq 38$
- $9x_0 + 7x_1 + 1x_2 \geq 34$
- $9x_0 + 7x_1 + 1x_2 \geq 34$
- $-7x_0^2 + 8x_1^2 \geq 0$
- $7x_0 + 3x_1 \leq 39$
- $7x_0^2 + 3x_1^2 + 3x_2^2 \leq 64$
- $10x_1 + 9x_2 \leq 43$
- $1x_0 + 10x_1 + 9x_2 \leq 58$

## 5: Create the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by Laura'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Paul')],
    'objective_function': '4*x0^2 + 8*x0*x1 + 2*x1*x2 + 2*x2^2 + 4*x2',
    'constraints': [
        '7*x0 <= 76',
        '1*x0 <= 82',
        '9*x0 <= 130',
        '3*x1 <= 76',
        '10*x1 <= 82',
        '7*x1 <= 130',
        '3*x2 <= 76',
        '9*x2 <= 82',
        '1*x2 <= 130',
        '7*x0^2 + 3*x1^2 >= 24',
        '7*x0 + 3*x2 >= 23',
        '7*x0^2 + 3*x1^2 + 3*x2^2 >= 23',
        '7*x0 + 3*x1 + 3*x2 >= 23',
        '1*x0^2 + 10*x1^2 >= 19',
        '10*x1 + 9*x2 >= 26',
        '1*x0 + 10*x1 + 9*x2 >= 26',
        '7*x1 + 1*x2 >= 22',
        '9*x0^2 + 7*x1^2 >= 38',
        '9*x0 + 7*x1 + 1*x2 >= 34',
        '9*x0 + 7*x1 + 1*x2 >= 34',
        '-7*x0^2 + 8*x1^2 >= 0',
        '7*x0 + 3*x1 <= 39',
        '7*x0^2 + 3*x1^2 + 3*x2^2 <= 64',
        '10*x1 + 9*x2 <= 43',
        '1*x0 + 10*x1 + 9*x2 <= 58'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='hours_worked_by_Laura')
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='hours_worked_by_George')
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='hours_worked_by_Paul')

    # Define the objective function
    model.setObjective(4*x0**2 + 8*x0*x1 + 2*x1*x2 + 2*x2**2 + 4*x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(7*x0 <= 76)
    model.addConstr(1*x0 <= 82)
    model.addConstr(9*x0 <= 130)
    model.addConstr(3*x1 <= 76)
    model.addConstr(10*x1 <= 82)
    model.addConstr(7*x1 <= 130)
    model.addConstr(3*x2 <= 76)
    model.addConstr(9*x2 <= 82)
    model.addConstr(1*x2 <= 130)
    model.addConstr(7*x0**2 + 3*x1**2 >= 24)
    model.addConstr(7*x0 + 3*x2 >= 23)
    model.addConstr(7*x0**2 + 3*x1**2 + 3*x2**2 >= 23)
    model.addConstr(7*x0 + 3*x1 + 3*x2 >= 23)
    model.addConstr(1*x0**2 + 10*x1**2 >= 19)
    model.addConstr(10*x1 + 9*x2 >= 26)
    model.addConstr(1*x0 + 10*x1 + 9*x2 >= 26)
    model.addConstr(7*x1 + 1*x2 >= 22)
    model.addConstr(9*x0**2 + 7*x1**2 >= 38)
    model.addConstr(9*x0 + 7*x1 + 1*x2 >= 34)
    model.addConstr(9*x0 + 7*x1 + 1*x2 >= 34)
    model.addConstr(-7*x0**2 + 8*x1**2 >= 0)
    model.addConstr(7*x0 + 3*x1 <= 39)
    model.addConstr(7*x0**2 + 3*x1**2 + 3*x2**2 <= 64)
    model.addConstr(10*x1 + 9*x2 <= 43)
    model.addConstr(1*x0 + 10*x1 + 9*x2 <= 58)

    # Optimize the model
    model.optimize()

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

optimize_problem()
```