To solve the optimization problem described, we will use the Gurobi Python API to model and solve the linear programming problem. The problem involves minimizing an objective function subject to several constraints.

First, let's break down the problem into its components:
- Decision variables: hours worked by Laura (L), hours worked by Hank (H), and hours worked by Mary (M).
- Objective function: Minimize 2.81*L + 5.39*H + 8.18*M.
- Constraints:
  - Likelihood to quit index constraints for each individual.
  - Organization score constraints for each pair and the trio of workers.
  - Additional linear constraints involving hours worked by each worker.

Given that all variables can be fractional, we treat them as continuous variables in our model.

Here's how we translate this problem into Gurobi Python code:

```python
from gurobipy import *

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

# Decision variables: hours worked by each person
L = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Laura")
H = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Hank")
M = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Mary")

# Objective function: minimize
m.setObjective(2.81*L + 5.39*H + 8.18*M, GRB.MINIMIZE)

# Constraints
# Likelihood to quit index constraints (note: these seem to be individual properties rather than constraints)
# Thus, they might not directly translate into constraints but could influence the objective or other constraints

# Total combined likelihood to quit index from hours worked by Laura plus hours worked by Hank >= 20
m.addConstr(23.08*L + 9.62*H >= 20, name="likelihood_to_quit_index_LH")

# Total combined likelihood to quit index from hours worked by Laura, hours worked by Hank, and hours worked by Mary >= 20
m.addConstr(23.08*L + 9.62*H + 8.92*M >= 20, name="likelihood_to_quit_index_LHM")

# Organization score constraints
# Total combined organization score from hours worked by Laura and hours worked by Hank >= 23
m.addConstr(20.84*L + 17.17*H >= 23, name="organization_score_LH")

# Total combined organization score from hours worked by Laura and hours worked by Mary >= 44
m.addConstr(20.84*L + 20.23*M >= 44, name="organization_score_LM")

# Total combined organization score from hours worked by Laura, hours worked by Hank, and hours worked by Mary >= 44
m.addConstr(20.84*L + 17.17*H + 20.23*M >= 44, name="organization_score_LHM")

# Additional constraints
# -10 times the number of hours worked by Hank plus 5 times the number of hours worked by Mary >= 0
m.addConstr(-10*H + 5*M >= 0, name="additional_constraint_1")

# -8 times the number of hours worked by Laura plus 1 times the number of hours worked by Hank >= 0
m.addConstr(-8*L + H >= 0, name="additional_constraint_2")

# Total combined organization score from hours worked by Laura, hours worked by Hank, and hours worked by Mary <= 150
m.addConstr(20.84*L + 17.17*H + 20.23*M <= 150, name="organization_score_LHM_upper_bound")

# Optimize the model
m.optimize()

# Print 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 Mary: {M.x}")
else:
    print("No optimal solution found")
```