To solve the given optimization problem, we first need to understand the objective function and the constraints. The objective is to maximize the value of \(4.64 \times \text{hours worked by Laura} + 3.55 \times \text{hours worked by Hank} + 9.46 \times \text{hours worked by Paul} + 7.42 \times \text{hours worked by Peggy}\).

The constraints are based on the paperwork competence ratings of each individual and their combinations, ensuring that these do not exceed certain thresholds.

Given:
- Objective function: \(4.64L + 3.55H + 9.46P + 7.42G\), where \(L\), \(H\), \(P\), and \(G\) represent the hours worked by Laura, Hank, Paul, and Peggy, respectively.
- Constraints:
  - \(5H + 6G \leq 210\)
  - \(26P + 6G \leq 210\)
  - \(17L + 26P \leq 142\)
  - \(17L + 6G \leq 232\)
  - \(17L + 5H + 26P + 6G \leq 250\) (Note: This constraint was initially misstated as part of the resources/attributes but seems to be a constraint based on the context)

All variables (\(L\), \(H\), \(P\), \(G\)) are non-negative and can be fractional.

Here is how you could model this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define the variables
L = m.addVar(lb=0, name="hours_worked_by_Laura")
H = m.addVar(lb=0, name="hours_worked_by_Hank")
P = m.addVar(lb=0, name="hours_worked_by_Paul")
G = m.addVar(lb=0, name="hours_worked_by_Peggy")

# Define the objective function
m.setObjective(4.64*L + 3.55*H + 9.46*P + 7.42*G, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*H + 6*G <= 210, name="Constraint_1")
m.addConstr(26*P + 6*G <= 210, name="Constraint_2")
m.addConstr(17*L + 26*P <= 142, name="Constraint_3")
m.addConstr(17*L + 6*G <= 232, name="Constraint_4")
m.addConstr(17*L + 5*H + 26*P + 6*G <= 250, name="Total_Competence_Constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Laura: {L.x}")
    print(f"Hours worked by Hank: {H.x}")
    print(f"Hours worked by Paul: {P.x}")
    print(f"Hours worked by Peggy: {G.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```