## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Bobby', 'hours worked by Hank', 'hours worked by George', 'hours worked by Paul']. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $9x_0 + 9x_1 + 9x_2 + 5x_3$.

## Step 3: List the constraints
- $12.31x_0 \leq 135$
- $6.47x_0 \leq 164$
- $5.88x_1 \leq 135$
- $7.82x_1 \leq 164$
- $14.3x_2 \leq 135$
- $6.71x_2 \leq 164$
- $12.49x_3 \leq 135$
- $11.73x_3 \leq 164$
- $5.88x_1 + 14.3x_2 \geq 30$
- $12.31x_0 + 5.88x_1 \geq 27$
- $14.3x_2 + 12.49x_3 \geq 27$
- $6.71x_2 + 11.73x_3 \geq 14$
- $7.82x_1 + 11.73x_3 \geq 24$
- $7.82x_1 + 6.71x_2 + 11.73x_3 \geq 40$
- $6.47x_0 + 7.82x_1 + 11.73x_3 \geq 40$
- $6.47x_0 + 7.82x_1 + 6.71x_2 \geq 40$
- $7.82x_1 + 6.71x_2 + 11.73x_3 \geq 40$
- $6.47x_0 + 7.82x_1 + 11.73x_3 \geq 40$
- $6.47x_0 + 7.82x_1 + 6.71x_2 \geq 40$
- $7.82x_1 + 6.71x_2 + 11.73x_3 \geq 22$
- $6.47x_0 + 7.82x_1 + 11.73x_3 \geq 22$
- $6.47x_0 + 7.82x_1 + 6.71x_2 \geq 22$
- $5.88x_1 + 14.3x_2 \leq 76$
- $12.31x_0 + 5.88x_1 \leq 68$
- $12.31x_0 + 14.3x_2 \leq 99$
- $12.31x_0 + 5.88x_1 + 14.3x_2 + 12.49x_3 \leq 99$
- $6.47x_0 + 6.71x_2 \leq 65$
- $7.82x_1 + 11.73x_3 \leq 141$
- $6.71x_2 + 11.73x_3 \leq 123$
- $7.82x_1 + 6.71x_2 + 11.73x_3 \leq 145$
- $6.47x_0 + 7.82x_1 + 6.71x_2 + 11.73x_3 \leq 145$

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="x0", lb=0)  # hours worked by Bobby
x1 = model.addVar(name="x1", lb=0)  # hours worked by Hank
x2 = model.addVar(name="x2", lb=0)  # hours worked by George
x3 = model.addVar(name="x3", lb=0)  # hours worked by Paul

# Define the objective function
model.setObjective(9 * x0 + 9 * x1 + 9 * x2 + 5 * x3, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(12.31 * x0 <= 135)
model.addConstr(6.47 * x0 <= 164)
model.addConstr(5.88 * x1 <= 135)
model.addConstr(7.82 * x1 <= 164)
model.addConstr(14.3 * x2 <= 135)
model.addConstr(6.71 * x2 <= 164)
model.addConstr(12.49 * x3 <= 135)
model.addConstr(11.73 * x3 <= 164)
model.addConstr(5.88 * x1 + 14.3 * x2 >= 30)
model.addConstr(12.31 * x0 + 5.88 * x1 >= 27)
model.addConstr(14.3 * x2 + 12.49 * x3 >= 27)
model.addConstr(6.71 * x2 + 11.73 * x3 >= 14)
model.addConstr(7.82 * x1 + 11.73 * x3 >= 24)
model.addConstr(7.82 * x1 + 6.71 * x2 + 11.73 * x3 >= 40)
model.addConstr(6.47 * x0 + 7.82 * x1 + 11.73 * x3 >= 40)
model.addConstr(6.47 * x0 + 7.82 * x1 + 6.71 * x2 >= 40)
model.addConstr(7.82 * x1 + 6.71 * x2 + 11.73 * x3 >= 40)
model.addConstr(6.47 * x0 + 7.82 * x1 + 11.73 * x3 >= 40)
model.addConstr(6.47 * x0 + 7.82 * x1 + 6.71 * x2 >= 40)
model.addConstr(7.82 * x1 + 6.71 * x2 + 11.73 * x3 >= 22)
model.addConstr(6.47 * x0 + 7.82 * x1 + 11.73 * x3 >= 22)
model.addConstr(6.47 * x0 + 7.82 * x1 + 6.71 * x2 >= 22)
model.addConstr(5.88 * x1 + 14.3 * x2 <= 76)
model.addConstr(12.31 * x0 + 5.88 * x1 <= 68)
model.addConstr(12.31 * x0 + 14.3 * x2 <= 99)
model.addConstr(12.31 * x0 + 5.88 * x1 + 14.3 * x2 + 12.49 * x3 <= 99)
model.addConstr(6.47 * x0 + 6.71 * x2 <= 65)
model.addConstr(7.82 * x1 + 11.73 * x3 <= 141)
model.addConstr(6.71 * x2 + 11.73 * x3 <= 123)
model.addConstr(7.82 * x1 + 6.71 * x2 + 11.73 * x3 <= 145)
model.addConstr(6.47 * x0 + 7.82 * x1 + 6.71 * x2 + 11.73 * x3 <= 145)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Hours worked by Bobby: ", x0.varValue)
    print("Hours worked by Hank: ", x1.varValue)
    print("Hours worked by George: ", x2.varValue)
    print("Hours worked by Paul: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bobby'), 
        ('x1', 'hours worked by Hank'), 
        ('x2', 'hours worked by George'), 
        ('x3', 'hours worked by Paul')
    ], 
    'objective_function': '9*x0 + 9*x1 + 9*x2 + 5*x3', 
    'constraints': [
        '12.31*x0 <= 135',
        '6.47*x0 <= 164',
        '5.88*x1 <= 135',
        '7.82*x1 <= 164',
        '14.3*x2 <= 135',
        '6.71*x2 <= 164',
        '12.49*x3 <= 135',
        '11.73*x3 <= 164',
        '5.88*x1 + 14.3*x2 >= 30',
        '12.31*x0 + 5.88*x1 >= 27',
        '14.3*x2 + 12.49*x3 >= 27',
        '6.71*x2 + 11.73*x3 >= 14',
        '7.82*x1 + 11.73*x3 >= 24',
        '7.82*x1 + 6.71*x2 + 11.73*x3 >= 40',
        '6.47*x0 + 7.82*x1 + 11.73*x3 >= 40',
        '6.47*x0 + 7.82*x1 + 6.71*x2 >= 40',
        '7.82*x1 + 6.71*x2 + 11.73*x3 >= 40',
        '6.47*x0 + 7.82*x1 + 11.73*x3 >= 40',
        '6.47*x0 + 7.82*x1 + 6.71*x2 >= 40',
        '7.82*x1 + 6.71*x2 + 11.73*x3 >= 22',
        '6.47*x0 + 7.82*x1 + 11.73*x3 >= 22',
        '6.47*x0 + 7.82*x1 + 6.71*x2 >= 22',
        '5.88*x1 + 14.3*x2 <= 76',
        '12.31*x0 + 5.88*x1 <= 68',
        '12.31*x0 + 14.3*x2 <= 99',
        '12.31*x0 + 5.88*x1 + 14.3*x2 + 12.49*x3 <= 99',
        '6.47*x0 + 6.71*x2 <= 65',
        '7.82*x1 + 11.73*x3 <= 141',
        '6.71*x2 + 11.73*x3 <= 123',
        '7.82*x1 + 6.71*x2 + 11.73*x3 <= 145',
        '6.47*x0 + 7.82*x1 + 6.71*x2 + 11.73*x3 <= 145'
    ]
}
```