## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'hours worked by Laura', 'hours worked by Bill', 'hours worked by Paul', and 'hours worked by George', which we can denote as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $5x_0 + 2x_1 + 5x_2 + 7x_3$.

## 3: List the constraints in symbolic notation
The constraints given are:
- $8.22x_1 + 11.31x_3 \geq 39$
- $8.35x_0 + 9.77x_2 \geq 12$
- $8.35x_0 + 4.64x_1 \geq 13$
- $2.91x_2 + 1.13x_3 \geq 26$
- $1.15x_1 + 0.49x_2 \geq 7$
- $0.8x_0 + 0.49x_2 \geq 16$
- $0.8x_0 + 1.15x_1 \geq 7$
- $10x_1 - 9x_2 - 10x_3 \geq 0$
- $8.22x_1 + 11.31x_3 \leq 68$
- $1.09x_0 + 10.62x_2 \leq 139$
- $8.22x_1 + 2.91x_2 \leq 207$
- $1.09x_0 + 8.22x_1 \leq 126$
- $1.09x_0 + 10.62x_2 + 11.31x_3 \leq 71$
- $1.09x_0 + 8.22x_1 + 10.62x_2 + 11.31x_3 \leq 71$
- $4.64x_1 + 9.77x_2 \leq 83$
- $9.77x_2 + 4.76x_3 \leq 43$
- $8.35x_0 + 4.64x_1 + 9.77x_2 + 4.76x_3 \leq 43$
- $0.95x_0 + 2.91x_2 \leq 182$
- $0.95x_0 + 1.13x_3 \leq 180$
- $2.91x_2 + 1.13x_3 \leq 164$
- $6.37x_1 + 2.91x_2 \leq 149$
- $0.95x_0 + 6.37x_1 + 2.91x_2 + 1.13x_3 \leq 149$
- $0.49x_2 + 7.4x_3 \leq 33$
- $1.15x_1 + 0.49x_2 \leq 54$
- $0.8x_0 + 0.49x_2 + 7.4x_3 \leq 26$
- $0.8x_0 + 1.15x_1 + 7.4x_3 \leq 23$
- $1.15x_1 + 0.49x_2 + 7.4x_3 \leq 65$
- $0.8x_0 + 1.15x_1 + 0.49x_2 \leq 19$
- $0.8x_0 + 1.15x_1 + 0.49x_2 + 7.4x_3 \leq 19$
- $x_0$ is an integer.

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Laura'),
        ('x1', 'hours worked by Bill'),
        ('x2', 'hours worked by Paul'),
        ('x3', 'hours worked by George')
    ],
    'objective_function': '5*x0 + 2*x1 + 5*x2 + 7*x3',
    'constraints': [
        '8.22*x1 + 11.31*x3 >= 39',
        '8.35*x0 + 9.77*x2 >= 12',
        '8.35*x0 + 4.64*x1 >= 13',
        '2.91*x2 + 1.13*x3 >= 26',
        '1.15*x1 + 0.49*x2 >= 7',
        '0.8*x0 + 0.49*x2 >= 16',
        '0.8*x0 + 1.15*x1 >= 7',
        '10*x1 - 9*x2 - 10*x3 >= 0',
        '8.22*x1 + 11.31*x3 <= 68',
        '1.09*x0 + 10.62*x2 <= 139',
        '8.22*x1 + 2.91*x2 <= 207',
        '1.09*x0 + 8.22*x1 <= 126',
        '1.09*x0 + 10.62*x2 + 11.31*x3 <= 71',
        '1.09*x0 + 8.22*x1 + 10.62*x2 + 11.31*x3 <= 71',
        '4.64*x1 + 9.77*x2 <= 83',
        '9.77*x2 + 4.76*x3 <= 43',
        '8.35*x0 + 4.64*x1 + 9.77*x2 + 4.76*x3 <= 43',
        '0.95*x0 + 2.91*x2 <= 182',
        '0.95*x0 + 1.13*x3 <= 180',
        '2.91*x2 + 1.13*x3 <= 164',
        '6.37*x1 + 2.91*x2 <= 149',
        '0.95*x0 + 6.37*x1 + 2.91*x2 + 1.13*x3 <= 149',
        '0.49*x2 + 7.4*x3 <= 33',
        '1.15*x1 + 0.49*x2 <= 54',
        '0.8*x0 + 0.49*x2 + 7.4*x3 <= 26',
        '0.8*x0 + 1.15*x1 + 7.4*x3 <= 23',
        '1.15*x1 + 0.49*x2 + 7.4*x3 <= 65',
        '0.8*x0 + 1.15*x1 + 0.49*x2 <= 19',
        '0.8*x0 + 1.15*x1 + 0.49*x2 + 7.4*x3 <= 19',
        'x0 % 1 == 0'
    ]
}
```

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

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name='x0', vtype=gp.GRB.INTEGER)  # hours worked by Laura
x1 = m.addVar(name='x1')  # hours worked by Bill
x2 = m.addVar(name='x2')  # hours worked by Paul
x3 = m.addVar(name='x3')  # hours worked by George

# Define the objective function
m.setObjective(5 * x0 + 2 * x1 + 5 * x2 + 7 * x3, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(8.22 * x1 + 11.31 * x3 >= 39)
m.addConstr(8.35 * x0 + 9.77 * x2 >= 12)
m.addConstr(8.35 * x0 + 4.64 * x1 >= 13)
m.addConstr(2.91 * x2 + 1.13 * x3 >= 26)
m.addConstr(1.15 * x1 + 0.49 * x2 >= 7)
m.addConstr(0.8 * x0 + 0.49 * x2 >= 16)
m.addConstr(0.8 * x0 + 1.15 * x1 >= 7)
m.addConstr(10 * x1 - 9 * x2 - 10 * x3 >= 0)
m.addConstr(8.22 * x1 + 11.31 * x3 <= 68)
m.addConstr(1.09 * x0 + 10.62 * x2 <= 139)
m.addConstr(8.22 * x1 + 2.91 * x2 <= 207)
m.addConstr(1.09 * x0 + 8.22 * x1 <= 126)
m.addConstr(1.09 * x0 + 10.62 * x2 + 11.31 * x3 <= 71)
m.addConstr(1.09 * x0 + 8.22 * x1 + 10.62 * x2 + 11.31 * x3 <= 71)
m.addConstr(4.64 * x1 + 9.77 * x2 <= 83)
m.addConstr(9.77 * x2 + 4.76 * x3 <= 43)
m.addConstr(8.35 * x0 + 4.64 * x1 + 9.77 * x2 + 4.76 * x3 <= 43)
m.addConstr(0.95 * x0 + 2.91 * x2 <= 182)
m.addConstr(0.95 * x0 + 1.13 * x3 <= 180)
m.addConstr(2.91 * x2 + 1.13 * x3 <= 164)
m.addConstr(6.37 * x1 + 2.91 * x2 <= 149)
m.addConstr(0.95 * x0 + 6.37 * x1 + 2.91 * x2 + 1.13 * x3 <= 149)
m.addConstr(0.49 * x2 + 7.4 * x3 <= 33)
m.addConstr(1.15 * x1 + 0.49 * x2 <= 54)
m.addConstr(0.8 * x0 + 0.49 * x2 + 7.4 * x3 <= 26)
m.addConstr(0.8 * x0 + 1.15 * x1 + 7.4 * x3 <= 23)
m.addConstr(1.15 * x1 + 0.49 * x2 + 7.4 * x3 <= 65)
m.addConstr(0.8 * x0 + 1.15 * x1 + 0.49 * x2 <= 19)
m.addConstr(0.8 * x0 + 1.15 * x1 + 0.49 * x2 + 7.4 * x3 <= 19)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('x0: ', x0.varValue)
    print('x1: ', x1.varValue)
    print('x2: ', x2.varValue)
    print('x3: ', x3.varValue)
else:
    print('No solution found')
```