## Step 1: Define the variables and their corresponding attributes
The variables are 'hours worked by George', 'hours worked by Paul', 'hours worked by Peggy', 'hours worked by Jean', and 'hours worked by Bill'. Let's denote them as $x_0$, $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Define the objective function
The objective function to maximize is $8x_0 + 6x_1 + 1x_2 + 9x_3 + 9x_4$.

## Step 3: List all the constraints
The constraints are:
- $3x_0 \geq 3$
- $1x_0 \geq 1$
- $3x_0 \geq 3$
- $3x_1 \geq 3$
- $4x_1 \geq 4$
- $2x_1 \geq 2$
- $2x_2 \geq 2$
- $5x_2 \geq 5$
- $3x_2 \geq 3$
- $1x_3 \geq 1$
- $4x_3 \geq 4$
- $5x_3 \geq 5$
- $5x_4 \geq 5$
- $2x_4 \geq 2$
- $2x_4 \geq 2$
- $3x_0 + 1x_3 \geq 5$
- $3x_0 + 2x_2 + 1x_3 \geq 8$
- $3x_0 + 3x_1 + 2x_2 \geq 8$
- $3x_0 + 3x_1 + 1x_3 \geq 8$
- $3x_0 + 1x_3 + 5x_4 \geq 8$
- $3x_1 + 2x_2 + 5x_4 \geq 8$
- $2x_2 + 1x_3 + 5x_4 \geq 8$
- $3x_0 + 2x_2 + 1x_3 \geq 10$
- $3x_0 + 3x_1 + 2x_2 \geq 10$
- $3x_0 + 3x_1 + 1x_3 \geq 10$
- $3x_0 + 1x_3 + 5x_4 \geq 10$
- $3x_1 + 2x_2 + 5x_4 \geq 10$
- $2x_2 + 1x_3 + 5x_4 \geq 10$
- $3x_0 + 2x_2 + 1x_3 \geq 12$
- $3x_0 + 3x_1 + 2x_2 \geq 12$
- $3x_0 + 3x_1 + 1x_3 \geq 12$
- $3x_0 + 1x_3 + 5x_4 \geq 12$
- $3x_1 + 2x_2 + 5x_4 \geq 12$
- $2x_2 + 1x_3 + 5x_4 \geq 12$
- $3x_0 + 2x_2 + 1x_3 \geq 15$
- $3x_0 + 3x_1 + 2x_2 \geq 15$
- $3x_0 + 3x_1 + 1x_3 \geq 15$
- $3x_0 + 1x_3 + 5x_4 \geq 15$
- $3x_1 + 2x_2 + 5x_4 \geq 15$
- $2x_2 + 1x_3 + 5x_4 \geq 15$
- $3x_0 + 3x_1 + 1x_2 \leq 77$
- $3x_1 + 5x_2 \leq 78$
- $3x_0 + 5x_4 \leq 64$
- $3x_1 + 2x_4 \leq 64$
- $3x_0 + 2x_2 \leq 64$
- $3x_3 + 2x_4 \leq 35$
- $3x_2 + 5x_3 \leq 28$
- $2x_1 + 3x_2 \leq 57$
- $3x_2 + 2x_4 \leq 58$
- $3x_0 + 6x_1 + 3x_2 + 5x_3 + 2x_4 \leq 58$

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

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # hours worked by George
x1 = m.addVar(name="x1", lb=0)  # hours worked by Paul
x2 = m.addVar(name="x2", lb=0)  # hours worked by Peggy
x3 = m.addVar(name="x3", lb=0)  # hours worked by Jean
x4 = m.addVar(name="x4", lb=0)  # hours worked by Bill

# Define the objective function
m.setObjective(8*x0 + 6*x1 + x2 + 9*x3 + 9*x4, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x0 >= 3)
m.addConstr(x0 >= 1)
m.addConstr(3*x0 >= 3)
m.addConstr(3*x1 >= 3)
m.addConstr(4*x1 >= 4)
m.addConstr(2*x1 >= 2)
m.addConstr(2*x2 >= 2)
m.addConstr(5*x2 >= 5)
m.addConstr(3*x2 >= 3)
m.addConstr(x3 >= 1)
m.addConstr(4*x3 >= 4)
m.addConstr(5*x3 >= 5)
m.addConstr(5*x4 >= 5)
m.addConstr(2*x4 >= 2)
m.addConstr(2*x4 >= 2)
m.addConstr(3*x0 + x3 >= 5)
m.addConstr(3*x0 + 2*x2 + x3 >= 8)
m.addConstr(3*x0 + 3*x1 + 2*x2 >= 8)
m.addConstr(3*x0 + 3*x1 + x3 >= 8)
m.addConstr(3*x0 + x3 + 5*x4 >= 8)
m.addConstr(3*x1 + 2*x2 + 5*x4 >= 8)
m.addConstr(2*x2 + x3 + 5*x4 >= 8)
m.addConstr(3*x0 + 2*x2 + x3 >= 10)
m.addConstr(3*x0 + 3*x1 + 2*x2 >= 10)
m.addConstr(3*x0 + 3*x1 + x3 >= 10)
m.addConstr(3*x0 + x3 + 5*x4 >= 10)
m.addConstr(3*x1 + 2*x2 + 5*x4 >= 10)
m.addConstr(2*x2 + x3 + 5*x4 >= 10)
m.addConstr(3*x0 + 2*x2 + x3 >= 12)
m.addConstr(3*x0 + 3*x1 + 2*x2 >= 12)
m.addConstr(3*x0 + 3*x1 + x3 >= 12)
m.addConstr(3*x0 + x3 + 5*x4 >= 12)
m.addConstr(3*x1 + 2*x2 + 5*x4 >= 12)
m.addConstr(2*x2 + x3 + 5*x4 >= 12)
m.addConstr(3*x0 + 2*x2 + x3 >= 15)
m.addConstr(3*x0 + 3*x1 + 2*x2 >= 15)
m.addConstr(3*x0 + 3*x1 + x3 >= 15)
m.addConstr(3*x0 + x3 + 5*x4 >= 15)
m.addConstr(3*x1 + 2*x2 + 5*x4 >= 15)
m.addConstr(2*x2 + x3 + 5*x4 >= 15)

m.addConstr(3*x0 + 3*x1 + x2 <= 77)
m.addConstr(3*x1 + 5*x2 <= 78)
m.addConstr(3*x0 + 5*x4 <= 64)
m.addConstr(3*x1 + 2*x4 <= 64)
m.addConstr(3*x0 + 2*x2 <= 64)
m.addConstr(x3 + 2*x4 <= 35)
m.addConstr(3*x2 + 5*x3 <= 28)
m.addConstr(2*x1 + 3*x2 <= 57)
m.addConstr(3*x2 + 2*x4 <= 58)
m.addConstr(3*x0 + 6*x1 + 3*x2 + 5*x3 + 2*x4 <= 58)

# 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)
    print("x4: ", x4.varValue)
else:
    print("No optimal solution found")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by George'),
        ('x1', 'hours worked by Paul'),
        ('x2', 'hours worked by Peggy'),
        ('x3', 'hours worked by Jean'),
        ('x4', 'hours worked by Bill')
    ],
    'objective_function': '8*x0 + 6*x1 + x2 + 9*x3 + 9*x4',
    'constraints': [
        '3*x0 >= 3',
        'x0 >= 1',
        '3*x0 >= 3',
        '3*x1 >= 3',
        '4*x1 >= 4',
        '2*x1 >= 2',
        '2*x2 >= 2',
        '5*x2 >= 5',
        '3*x2 >= 3',
        'x3 >= 1',
        '4*x3 >= 4',
        '5*x3 >= 5',
        '5*x4 >= 5',
        '2*x4 >= 2',
        '2*x4 >= 2',
        '3*x0 + x3 >= 5',
        '3*x0 + 2*x2 + x3 >= 8',
        '3*x0 + 3*x1 + 2*x2 >= 8',
        '3*x0 + 3*x1 + x3 >= 8',
        '3*x0 + x3 + 5*x4 >= 8',
        '3*x1 + 2*x2 + 5*x4 >= 8',
        '2*x2 + x3 + 5*x4 >= 8',
        '3*x0 + 2*x2 + x3 >= 10',
        '3*x0 + 3*x1 + 2*x2 >= 10',
        '3*x0 + 3*x1 + x3 >= 10',
        '3*x0 + x3 + 5*x4 >= 10',
        '3*x1 + 2*x2 + 5*x4 >= 10',
        '2*x2 + x3 + 5*x4 >= 10',
        '3*x0 + 2*x2 + x3 >= 12',
        '3*x0 + 3*x1 + 2*x2 >= 12',
        '3*x0 + 3*x1 + x3 >= 12',
        '3*x0 + x3 + 5*x4 >= 12',
        '3*x1 + 2*x2 + 5*x4 >= 12',
        '2*x2 + x3 + 5*x4 >= 12',
        '3*x0 + 2*x2 + x3 >= 15',
        '3*x0 + 3*x1 + 2*x2 >= 15',
        '3*x0 + 3*x1 + x3 >= 15',
        '3*x0 + x3 + 5*x4 >= 15',
        '3*x1 + 2*x2 + 5*x4 >= 15',
        '2*x2 + x3 + 5*x4 >= 15',
        '3*x0 + 3*x1 + x2 <= 77',
        '3*x1 + 5*x2 <= 78',
        '3*x0 + 5*x4 <= 64',
        '3*x1 + 2*x4 <= 64',
        '3*x0 + 2*x2 <= 64',
        'x3 + 2*x4 <= 35',
        '3*x2 + 5*x3 <= 28',
        '2*x1 + 3*x2 <= 57',
        '3*x2 + 2*x4 <= 58',
        '3*x0 + 6*x1 + 3*x2 + 5*x3 + 2*x4 <= 58'
    ]
}
```