## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Mary', 'hours worked by Dale', 'hours worked by Peggy', 'hours worked by Paul'].
Let's denote them as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $3x_1 + 4x_2 + 3x_3 + 8x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $2x_1 \leq 239$
- $6x_2 \leq 239$
- $4x_3 \leq 239$
- $17x_4 \leq 239$
- $2x_1 + 4x_3 + 17x_4 \geq 59$
- $2x_1 + 6x_2 + 4x_3 \geq 59$
- $2x_1 + 6x_2 + 17x_4 \geq 59$
- $2x_1 + 4x_3 + 17x_4 \geq 34$
- $2x_1 + 6x_2 + 4x_3 \geq 34$
- $2x_1 + 6x_2 + 17x_4 \geq 34$
- $2x_1 + 4x_3 + 17x_4 \geq 29$
- $2x_1 + 6x_2 + 4x_3 \geq 29$
- $2x_1 + 6x_2 + 17x_4 \geq 29$
- $6x_2 + 4x_3 \leq 73$
- $2x_1 + 4x_3 + 17x_4 \leq 124$
- $6x_2 + 4x_3 + 17x_4 \leq 118$
- $2x_1 + 6x_2 + 4x_3 \leq 69$
- $2x_1 + 6x_2 + 4x_3 + 17x_4 \leq 69$
- $x_1$ is an integer
- $x_2$ is not necessarily an integer
- $x_3$ is an integer
- $x_4$ is an integer

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

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

# Define the variables
x1 = m.addVar(name='x1', vtype='I')  # hours worked by Mary
x2 = m.addVar(name='x2')  # hours worked by Dale
x3 = m.addVar(name='x3', vtype='I')  # hours worked by Peggy
x4 = m.addVar(name='x4', vtype='I')  # hours worked by Paul

# Define the objective function
m.setObjective(3*x1 + 4*x2 + 3*x3 + 8*x4, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 <= 239)
m.addConstr(6*x2 <= 239)
m.addConstr(4*x3 <= 239)
m.addConstr(17*x4 <= 239)

m.addConstr(2*x1 + 4*x3 + 17*x4 >= 59)
m.addConstr(2*x1 + 6*x2 + 4*x3 >= 59)
m.addConstr(2*x1 + 6*x2 + 17*x4 >= 59)
m.addConstr(2*x1 + 4*x3 + 17*x4 >= 34)
m.addConstr(2*x1 + 6*x2 + 4*x3 >= 34)
m.addConstr(2*x1 + 6*x2 + 17*x4 >= 34)
m.addConstr(2*x1 + 4*x3 + 17*x4 >= 29)
m.addConstr(2*x1 + 6*x2 + 4*x3 >= 29)
m.addConstr(2*x1 + 6*x2 + 17*x4 >= 29)

m.addConstr(6*x2 + 4*x3 <= 73)
m.addConstr(2*x1 + 4*x3 + 17*x4 <= 124)
m.addConstr(6*x2 + 4*x3 + 17*x4 <= 118)
m.addConstr(2*x1 + 6*x2 + 4*x3 <= 69)
m.addConstr(2*x1 + 6*x2 + 4*x3 + 17*x4 <= 69)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Hours worked by Mary: ', x1.varValue)
    print('Hours worked by Dale: ', x2.varValue)
    print('Hours worked by Peggy: ', x3.varValue)
    print('Hours worked by Paul: ', x4.varValue)
else:
    print('No optimal solution found')
```

## Step 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Mary'), 
        ('x2', 'hours worked by Dale'), 
        ('x3', 'hours worked by Peggy'), 
        ('x4', 'hours worked by Paul')
    ], 
    'objective_function': '3*x1 + 4*x2 + 3*x3 + 8*x4', 
    'constraints': [
        '2*x1 <= 239', 
        '6*x2 <= 239', 
        '4*x3 <= 239', 
        '17*x4 <= 239', 
        '2*x1 + 4*x3 + 17*x4 >= 59', 
        '2*x1 + 6*x2 + 4*x3 >= 59', 
        '2*x1 + 6*x2 + 17*x4 >= 59', 
        '2*x1 + 4*x3 + 17*x4 >= 34', 
        '2*x1 + 6*x2 + 4*x3 >= 34', 
        '2*x1 + 6*x2 + 17*x4 >= 34', 
        '2*x1 + 4*x3 + 17*x4 >= 29', 
        '2*x1 + 6*x2 + 4*x3 >= 29', 
        '2*x1 + 6*x2 + 17*x4 >= 29', 
        '6*x2 + 4*x3 <= 73', 
        '2*x1 + 4*x3 + 17*x4 <= 124', 
        '6*x2 + 4*x3 + 17*x4 <= 118', 
        '2*x1 + 6*x2 + 4*x3 <= 69', 
        '2*x1 + 6*x2 + 4*x3 + 17*x4 <= 69'
    ]
}
```