## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Laura', 'hours worked by George', 'hours worked by Dale', and 'hours worked by Paul', which can be represented symbolically 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 $1.55x_1 + 3.23x_2 + 9.61x_3 + 1.91x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $13x_1 + 10x_3 \geq 26$
- $5x_2 + 11x_4 \leq 76$
- $10x_3 + 11x_4 \leq 57$
- $13x_1 + 5x_2 \leq 104$
- $5x_2 + 10x_3 \leq 94$
- $13x_1 + 10x_3 \leq 38$
- $13x_1 + 5x_2 + 10x_3 + 11x_4 \leq 38$
- $x_1$ is an integer
- $x_2$ is an integer
- $x_3$ is not necessarily an integer
- $x_4$ is an integer

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by George'), 
        ('x3', 'hours worked by Dale'), 
        ('x4', 'hours worked by Paul')
    ], 
    'objective_function': '1.55*x1 + 3.23*x2 + 9.61*x3 + 1.91*x4', 
    'constraints': [
        '13*x1 + 10*x3 >= 26', 
        '5*x2 + 11*x4 <= 76', 
        '10*x3 + 11*x4 <= 57', 
        '13*x1 + 5*x2 <= 104', 
        '5*x2 + 10*x3 <= 94', 
        '13*x1 + 10*x3 <= 38', 
        '13*x1 + 5*x2 + 10*x3 + 11*x4 <= 38'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="hours_worked_by_Laura", vtype=gp.GRB.INTEGER)  # Laura
x2 = m.addVar(name="hours_worked_by_George", vtype=gp.GRB.INTEGER)  # George
x3 = m.addVar(name="hours_worked_by_Dale")  # Dale
x4 = m.addVar(name="hours_worked_by_Paul", vtype=gp.GRB.INTEGER)  # Paul

# Define the objective function
m.setObjective(1.55 * x1 + 3.23 * x2 + 9.61 * x3 + 1.91 * x4, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(13 * x1 + 10 * x3 >= 26)
m.addConstr(5 * x2 + 11 * x4 <= 76)
m.addConstr(10 * x3 + 11 * x4 <= 57)
m.addConstr(13 * x1 + 5 * x2 <= 104)
m.addConstr(5 * x2 + 10 * x3 <= 94)
m.addConstr(13 * x1 + 10 * x3 <= 38)
m.addConstr(13 * x1 + 5 * x2 + 10 * x3 + 11 * x4 <= 38)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Laura: {x1.varValue}")
    print(f"Hours worked by George: {x2.varValue}")
    print(f"Hours worked by Dale: {x3.varValue}")
    print(f"Hours worked by Paul: {x4.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```