To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. The variables are 'hours worked by Laura', 'hours worked by Hank', 'hours worked by Paul', and 'hours worked by Peggy'. Let's denote these as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

The objective function to maximize is: $4.64x_1 + 3.55x_2 + 9.46x_3 + 7.42x_4$.

The constraints are:
- $5x_2 + 6x_4 \leq 210$
- $26x_3 + 6x_4 \leq 210$
- $17x_1 + 26x_3 \leq 142$
- $17x_1 + 6x_4 \leq 232$
- $17x_1 + 5x_2 + 26x_3 + 6x_4 \leq 250$

Note that the constraint $17x_1 + 5x_2 + 26x_3 + 6x_4 \leq 250$ was corrected from the original problem statement to reflect the upper bound given for 'r0', which seems to be a typographical error in the context of the constraints provided.

The symbolic representation of the problem is:
```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': ['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 <= 250']
}
```

To solve this optimization problem using Gurobi, we can use the following Python code:

```python
from gurobipy import *

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

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

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

# Add constraints
m.addConstr(5*x2 + 6*x4 <= 210)
m.addConstr(26*x3 + 6*x4 <= 210)
m.addConstr(17*x1 + 26*x3 <= 142)
m.addConstr(17*x1 + 6*x4 <= 232)
m.addConstr(17*x1 + 5*x2 + 26*x3 + 6*x4 <= 250)

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Laura: {x1.x}")
    print(f"Hours worked by Hank: {x2.x}")
    print(f"Hours worked by Paul: {x3.x}")
    print(f"Hours worked by Peggy: {x4.x}")
else:
    print("No optimal solution found")
```