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

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $7.08x_0 + 2.43x_1 + 4.45x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $15x_0 \leq 159$
- $2x_0 \leq 103$
- $7x_0 \leq 128$
- $6x_0 \leq 97$
- $4x_1 \leq 159$
- $6x_1 \leq 103$
- $12x_1 \leq 128$
- $8x_1 \leq 97$
- $12x_2 \leq 159$
- $10x_2 \leq 103$
- $6x_2 \leq 128$
- $4x_2 \leq 97$
- $15x_0 + 12x_2 \geq 38$
- $15x_0 + 4x_1 + 12x_2 \geq 53$
- $6x_0 + 4x_2 \geq 28$
- $6x_0 + 8x_1 + 4x_2 \geq 29$
- $4x_1 + 12x_2 \leq 156$
- $15x_0 + 4x_1 + 12x_2 \leq 156$
- $2x_0 + 10x_2 \leq 66$
- $2x_0 + 6x_1 + 10x_2 \leq 92$
- $7x_0 + 6x_2 \leq 100$
- $7x_0 + 12x_1 + 6x_2 \leq 100$
- $8x_1 + 4x_2 \leq 33$
- $6x_0 + 8x_1 + 4x_2 \leq 33$

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

# Create a new model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="hours_worked_by_Mary", lb=0)
x1 = model.addVar(name="hours_worked_by_George", lb=0)
x2 = model.addVar(name="hours_worked_by_Bill", lb=0)

# Define the objective function
model.setObjective(7.08 * x0 + 2.43 * x1 + 4.45 * x2, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(15 * x0 <= 159)
model.addConstr(2 * x0 <= 103)
model.addConstr(7 * x0 <= 128)
model.addConstr(6 * x0 <= 97)
model.addConstr(4 * x1 <= 159)
model.addConstr(6 * x1 <= 103)
model.addConstr(12 * x1 <= 128)
model.addConstr(8 * x1 <= 97)
model.addConstr(12 * x2 <= 159)
model.addConstr(10 * x2 <= 103)
model.addConstr(6 * x2 <= 128)
model.addConstr(4 * x2 <= 97)
model.addConstr(15 * x0 + 12 * x2 >= 38)
model.addConstr(15 * x0 + 4 * x1 + 12 * x2 >= 53)
model.addConstr(6 * x0 + 4 * x2 >= 28)
model.addConstr(6 * x0 + 8 * x1 + 4 * x2 >= 29)
model.addConstr(4 * x1 + 12 * x2 <= 156)
model.addConstr(15 * x0 + 4 * x1 + 12 * x2 <= 156)
model.addConstr(2 * x0 + 10 * x2 <= 66)
model.addConstr(2 * x0 + 6 * x1 + 10 * x2 <= 92)
model.addConstr(7 * x0 + 6 * x2 <= 100)
model.addConstr(7 * x0 + 12 * x1 + 6 * x2 <= 100)
model.addConstr(8 * x1 + 4 * x2 <= 33)
model.addConstr(6 * x0 + 8 * x1 + 4 * x2 <= 33)

# Optimize the model
model.optimize()

# Print the solution
print("Objective: ", model.objVal)
print("Hours worked by Mary: ", x0.varValue)
print("Hours worked by George: ", x1.varValue)
print("Hours worked by Bill: ", x2.varValue)

# Symbolic representation
sym_variables = [('x0', 'hours worked by Mary'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Bill')]
objective_function = '7.08*x0 + 2.43*x1 + 4.45*x2'
constraints = [
    '15*x0 <= 159',
    '2*x0 <= 103',
    '7*x0 <= 128',
    '6*x0 <= 97',
    '4*x1 <= 159',
    '6*x1 <= 103',
    '12*x1 <= 128',
    '8*x1 <= 97',
    '12*x2 <= 159',
    '10*x2 <= 103',
    '6*x2 <= 128',
    '4*x2 <= 97',
    '15*x0 + 12*x2 >= 38',
    '15*x0 + 4*x1 + 12*x2 >= 53',
    '6*x0 + 4*x2 >= 28',
    '6*x0 + 8*x1 + 4*x2 >= 29',
    '4*x1 + 12*x2 <= 156',
    '15*x0 + 4*x1 + 12*x2 <= 156',
    '2*x0 + 10*x2 <= 66',
    '2*x0 + 6*x1 + 10*x2 <= 92',
    '7*x0 + 6*x2 <= 100',
    '7*x0 + 12*x1 + 6*x2 <= 100',
    '8*x1 + 4*x2 <= 33',
    '6*x0 + 8*x1 + 4*x2 <= 33'
]

print("\nSymbolic Representation:")
print("Variables: ", sym_variables)
print("Objective Function: ", objective_function)
print("Constraints: ", constraints)
```

```json
{
    "sym_variables": [
        ["x0", "hours worked by Mary"],
        ["x1", "hours worked by George"],
        ["x2", "hours worked by Bill"]
    ],
    "objective_function": "7.08*x0 + 2.43*x1 + 4.45*x2",
    "constraints": [
        "15*x0 <= 159",
        "2*x0 <= 103",
        "7*x0 <= 128",
        "6*x0 <= 97",
        "4*x1 <= 159",
        "6*x1 <= 103",
        "12*x1 <= 128",
        "8*x1 <= 97",
        "12*x2 <= 159",
        "10*x2 <= 103",
        "6*x2 <= 128",
        "4*x2 <= 97",
        "15*x0 + 12*x2 >= 38",
        "15*x0 + 4*x1 + 12*x2 >= 53",
        "6*x0 + 4*x2 >= 28",
        "6*x0 + 8*x1 + 4*x2 >= 29",
        "4*x1 + 12*x2 <= 156",
        "15*x0 + 4*x1 + 12*x2 <= 156",
        "2*x0 + 10*x2 <= 66",
        "2*x0 + 6*x1 + 10*x2 <= 92",
        "7*x0 + 6*x2 <= 100",
        "7*x0 + 12*x1 + 6*x2 <= 100",
        "8*x1 + 4*x2 <= 33",
        "6*x0 + 8*x1 + 4*x2 <= 33"
    ]
}
```