To solve this optimization problem, we will first translate the given natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using mathematical notation.

Let's denote:
- \(x_1\) as the hours worked by Mary,
- \(x_2\) as the hours worked by Dale,
- \(x_3\) as the hours worked by Laura.

The objective function to minimize is given as: 
\[8.72x_1 + 5.55x_2 + 1.19x_3\]

The constraints are:
1. \(9.26x_1 \leq 108\)
2. \(4.77x_2 \leq 108\)
3. \(11.23x_3 \leq 108\)
4. \(4.77x_2 + 11.23x_3 \geq 34\)
5. \(9.26x_1 + 11.23x_3 \geq 29\)
6. \(9.26x_1 + 4.77x_2 + 11.23x_3 \geq 29\)
7. \(-4x_2 + 8x_3 \geq 0\)
8. \(9.26x_1 + 4.77x_2 \leq 43\)

Given the fractional hours worked are allowed, all variables are continuous.

Here is the symbolic representation of the problem:
```json
{
    'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Dale'), ('x3', 'hours worked by Laura')],
    'objective_function': '8.72*x1 + 5.55*x2 + 1.19*x3',
    'constraints': [
        '9.26*x1 <= 108',
        '4.77*x2 <= 108',
        '11.23*x3 <= 108',
        '4.77*x2 + 11.23*x3 >= 34',
        '9.26*x1 + 11.23*x3 >= 29',
        '9.26*x1 + 4.77*x2 + 11.23*x3 >= 29',
        '-4*x2 + 8*x3 >= 0',
        '9.26*x1 + 4.77*x2 <= 43'
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem:
```python
from gurobipy import *

# Create a new model
model = Model("Optimization_Problem")

# Add variables
x1 = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Mary")
x2 = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Dale")
x3 = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Laura")

# Set the objective function
model.setObjective(8.72*x1 + 5.55*x2 + 1.19*x3, GRB.MINIMIZE)

# Add constraints
model.addConstr(9.26*x1 <= 108)
model.addConstr(4.77*x2 <= 108)
model.addConstr(11.23*x3 <= 108)
model.addConstr(4.77*x2 + 11.23*x3 >= 34)
model.addConstr(9.26*x1 + 11.23*x3 >= 29)
model.addConstr(9.26*x1 + 4.77*x2 + 11.23*x3 >= 29)
model.addConstr(-4*x2 + 8*x3 >= 0)
model.addConstr(9.26*x1 + 4.77*x2 <= 43)

# Optimize the model
model.optimize()

# Print the solution
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Mary: {x1.x}")
    print(f"Hours worked by Dale: {x2.x}")
    print(f"Hours worked by Laura: {x3.x}")
else:
    print("No optimal solution found.")
```