To solve the optimization problem described, we need to minimize the objective function given while satisfying all constraints. The variables are 'hours worked by George' (G), 'hours worked by Bill' (B), and 'hours worked by Hank' (H). 

The objective function is: Minimize 9*G + 5*B + 9*H.

Constraints:
1. Likelihood to quit index for G, B, H are 1, 3, 4 respectively.
2. Dollar cost per hour for G, B, H are 3, 4, 1 respectively.
3. Combined likelihood to quit index constraints: 
   - G + H >= 19
   - G + B >= 24
   - G + B + H >= 24
4. Combined dollar cost per hour constraints:
   - 3*G + H >= 14 (Note: The original problem statement had an error in this constraint, assuming it should reflect the costs of George and Hank correctly)
   - 3*G + 4*B >= 6
   - 4*B + H >= 6
   - 3*G + 4*B + H >= 6
5. Additional constraints:
   - -8*B + 3*H >= 0
   - G + H <= 39 (upper bound for likelihood to quit index of George and Hank combined)
   - 3*G + H <= 53 (Note: Correcting the constraint based on dollar costs per hour, but it seems there was a misunderstanding in interpreting "no more than 53" as directly applying to the dollar cost equation which does not align with provided coefficients. This should reflect an accurate interpretation of given data.)
   - 3*G + 4*B + H <= 38 (Correcting for dollar costs per hour and their combined upper limit)

Given these constraints, we need to translate them into Gurobi code.

```python
from gurobipy import *

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

# Define variables
G = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_George")
B = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Bill")
H = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Hank")

# Objective function
m.setObjective(9*G + 5*B + 9*H, GRB.MINIMIZE)

# Constraints
m.addConstr(G + H >= 19, "likelihood_to_quit_GH")
m.addConstr(G + B >= 24, "likelihood_to_quit_GB")
m.addConstr(G + B + H >= 24, "likelihood_to_quit_GBH")

m.addConstr(3*G + H >= 14, "dollar_cost_GH") # Assuming this reflects the intention behind the problem statement
m.addConstr(3*G + 4*B >= 6, "dollar_cost_GB")
m.addConstr(4*B + H >= 6, "dollar_cost_BH")
m.addConstr(3*G + 4*B + H >= 6, "dollar_cost_GBH")

m.addConstr(-8*B + 3*H >= 0, "additional_constraint_1")
m.addConstr(G + H <= 39, "likelihood_to_quit_GH_upper_bound")
m.addConstr(3*G + H <= 53, "dollar_cost_GH_upper_bound") # Corrected based on provided coefficients and problem context
m.addConstr(3*G + 4*B + H <= 38, "dollar_cost_GBH_upper_bound")

# Optimize model
m.optimize()

# Print results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print(f"Objective: {m.objVal}")
```