To solve the given optimization problem using Gurobi, we first need to understand and translate the natural language description into a mathematical formulation that can be represented in code. The objective is to maximize the function:

9.01 * (hours worked by Hank) + 2.2 * (hours worked by Ringo) + 5.01 * (hours worked by Paul) + 4.0 * (hours worked by Laura)

Subject to various constraints involving the likelihood to quit indices for each worker and combinations thereof.

Let's denote:
- \(H\) as the hours worked by Hank,
- \(R\) as the hours worked by Ringo,
- \(P\) as the hours worked by Paul, and
- \(L\) as the hours worked by Laura.

The likelihood to quit indices are given as:
- Hank: 2
- Ringo: 13
- Paul: 13
- Laura: 8

Thus, the constraints can be formulated as follows:

1. \(2H + 13R + 13P + 8L \leq 130\) (Total likelihood to quit index constraint)
2. \(13R + 8L \geq 23\)
3. \(2H + 13P \geq 22\)
4. \(2H + 8L \geq 10\)
5. \(13R + 13P + 8L \geq 19\)
6. \(2H + 8L \leq 101\)
7. \(13P + 8L \leq 74\)
8. \(2H + 13P \leq 86\)
9. \(2H + 13R \leq 120\)
10. \(13R + 8L \leq 91\)
11. \(13R + 13P \leq 119\)
12. \(2H + 13R + 8L \leq 47\)
13. \(13R + 13P + 8L \leq 90\)
14. \(2H + 13R + 13P + 8L \leq 90\)

And the variables \(H\), \(R\), \(P\), and \(L\) must all be integers.

Here's how you could implement this in Gurobi using Python:

```python
from gurobipy import *

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

# Define the variables
H = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Hank")
R = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Ringo")
P = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Paul")
L = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Laura")

# Define the objective function
m.setObjective(9.01*H + 2.2*R + 5.01*P + 4.0*L, GRB.MAXIMIZE)

# Add constraints
m.addConstr(13*R + 8*L >= 23, name="constraint_1")
m.addConstr(2*H + 13*P >= 22, name="constraint_2")
m.addConstr(2*H + 8*L >= 10, name="constraint_3")
m.addConstr(13*R + 13*P + 8*L >= 19, name="constraint_4")
m.addConstr(2*H + 8*L <= 101, name="constraint_5")
m.addConstr(13*P + 8*L <= 74, name="constraint_6")
m.addConstr(2*H + 13*P <= 86, name="constraint_7")
m.addConstr(2*H + 13*R <= 120, name="constraint_8")
m.addConstr(13*R + 8*L <= 91, name="constraint_9")
m.addConstr(13*R + 13*P <= 119, name="constraint_10")
m.addConstr(2*H + 13*R + 8*L <= 47, name="constraint_11")
m.addConstr(13*R + 13*P + 8*L <= 90, name="constraint_12")
m.addConstr(2*H + 13*R + 13*P + 8*L <= 90, name="constraint_13")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print('Optimal solution found:')
    print('Hours worked by Hank:', H.x)
    print('Hours worked by Ringo:', R.x)
    print('Hours worked by Paul:', P.x)
    print('Hours worked by Laura:', L.x)
else:
    print('No optimal solution found')
```