To solve this optimization problem using Gurobi, we need to define the variables, objective function, and constraints according to the given description. 

First, let's clarify and simplify the problem statement by removing redundant or confusing parts:

- We have two decision variables: `hours_worked_by_Ringo` (which must be an integer) and `hours_worked_by_John` (which can be a fraction).
- The objective function to minimize is: `9 * hours_worked_by_Ringo + 2 * hours_worked_by_John`.
- Constraints:
  - Productivity rating constraint: `(6 * hours_worked_by_Ringo) + (12 * hours_worked_by_John) >= 52` and also at most 94.
  - Dollar cost per hour constraint: `(7 * hours_worked_by_Ringo) + (11 * hours_worked_by_John) >= 52` but at most 70.
  - Likelihood to quit index constraint: `(5 * hours_worked_by_Ringo) + (11 * hours_worked_by_John) >= 21` and also at most 61.
  - Paperwork competence rating constraint: `(9 * hours_worked_by_Ringo) + (14 * hours_worked_by_John) >= 21` but at most 37.
  - Another constraint: `-8 * hours_worked_by_Ringo + 5 * hours_worked_by_John >= 0`.

Now, let's write the Gurobi code to solve this problem:

```python
from gurobipy import *

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

# Define variables
hours_worked_by_Ringo = model.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Ringo")
hours_worked_by_John = model.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_John")

# Objective function
model.setObjective(9 * hours_worked_by_Ringo + 2 * hours_worked_by_John, GRB.MINIMIZE)

# Constraints
model.addConstr((6 * hours_worked_by_Ringo) + (12 * hours_worked_by_John) >= 52, name="productivity_min")
model.addConstr((6 * hours_worked_by_Ringo) + (12 * hours_worked_by_John) <= 94, name="productivity_max")

model.addConstr((7 * hours_worked_by_Ringo) + (11 * hours_worked_by_John) >= 52, name="dollar_cost_min")
model.addConstr((7 * hours_worked_by_Ringo) + (11 * hours_worked_by_John) <= 70, name="dollar_cost_max")

model.addConstr((5 * hours_worked_by_Ringo) + (11 * hours_worked_by_John) >= 21, name="quit_index_min")
model.addConstr((5 * hours_worked_by_Ringo) + (11 * hours_worked_by_John) <= 61, name="quit_index_max")

model.addConstr((9 * hours_worked_by_Ringo) + (14 * hours_worked_by_John) >= 21, name="paperwork_min")
model.addConstr((9 * hours_worked_by_Ringo) + (14 * hours_worked_by_John) <= 37, name="paperwork_max")

model.addConstr(-8 * hours_worked_by_Ringo + 5 * hours_worked_by_John >= 0, name="additional_constraint")

# Solve the model
model.optimize()

# Print solution if optimal
if model.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Ringo: {hours_worked_by_Ringo.X}")
    print(f"Hours worked by John: {hours_worked_by_John.X}")
else:
    print("No optimal solution found.")
```