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

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $4.64x_1 + 3.55x_2 + 9.46x_3 + 7.42x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $17x_1 \leq 250$
- $5x_2 \leq 250$
- $26x_3 \leq 250$
- $6x_4 \leq 250$
- $5x_2 + 6x_4 \leq 210$
- $26x_3 + 6x_4 \leq 210$
- $17x_1 + 26x_3 \leq 142$
- $17x_1 + 6x_4 \leq 232$
- $17x_1 + 5x_2 + 26x_3 + 6x_4 \leq 232$

## 4: Convert the problem into a Gurobi-compatible format
We will use Gurobi's Python API to model and solve this linear programming problem.

## 5: Write the Gurobi code
```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(name="hours_worked_by_Laura", lb=0)
x2 = m.addVar(name="hours_worked_by_Hank", lb=0)
x3 = m.addVar(name="hours_worked_by_Paul", lb=0)
x4 = m.addVar(name="hours_worked_by_Peggy", lb=0)

# Define the objective function
m.setObjective(4.64*x1 + 3.55*x2 + 9.46*x3 + 7.42*x4, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(17*x1 <= 250, name="Laura_paperwork")
m.addConstr(5*x2 <= 250, name="Hank_paperwork")
m.addConstr(26*x3 <= 250, name="Paul_paperwork")
m.addConstr(6*x4 <= 250, name="Peggy_paperwork")
m.addConstr(5*x2 + 6*x4 <= 210, name="Hank_Peggy_paperwork")
m.addConstr(26*x3 + 6*x4 <= 210, name="Paul_Peggy_paperwork")
m.addConstr(17*x1 + 26*x3 <= 142, name="Laura_Paul_paperwork")
m.addConstr(17*x1 + 6*x4 <= 232, name="Laura_Peggy_paperwork")
m.addConstr(17*x1 + 5*x2 + 26*x3 + 6*x4 <= 232, name="all_paperwork")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Laura: ", x1.varValue)
    print("Hours worked by Hank: ", x2.varValue)
    print("Hours worked by Paul: ", x3.varValue)
    print("Hours worked by Peggy: ", x4.varValue)
else:
    print("The model is infeasible")
```

## 6: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by Hank'), 
        ('x3', 'hours worked by Paul'), 
        ('x4', 'hours worked by Peggy')
    ], 
    'objective_function': '4.64*x1 + 3.55*x2 + 9.46*x3 + 7.42*x4', 
    'constraints': [
        '17*x1 <= 250', 
        '5*x2 <= 250', 
        '26*x3 <= 250', 
        '6*x4 <= 250', 
        '5*x2 + 6*x4 <= 210', 
        '26*x3 + 6*x4 <= 210', 
        '17*x1 + 26*x3 <= 142', 
        '17*x1 + 6*x4 <= 232', 
        '17*x1 + 5*x2 + 26*x3 + 6*x4 <= 232'
    ]
}
```