## Step 1: Define the optimization problem and identify the variables, objective function, and constraints.

The problem involves two variables: 'hours worked by Ringo' (let's denote it as $R$) and 'hours worked by John' (denoted as $J$). The objective function to minimize is $9R + 2J$.

## 2: List all the given constraints.

1. $R$ and $J$ must satisfy the following individual attribute constraints:
   - Productivity rating: $6R + 12J$
   - Dollar cost per hour: $7R + 11J$
   - Likelihood to quit index: $5R + 11J$
   - Paperwork competence rating: $9R + 14J$

2. Combined constraints:
   - Productivity rating: $6R + 12J \geq 52$
   - Dollar cost per hour: $7R + 11J \geq 52$
   - Likelihood to quit index: $5R + 11J \geq 21$
   - Paperwork competence rating: $9R + 14J \geq 21$

3. Additional constraints:
   - $6R + 12J \leq 94$
   - $7R + 11J \leq 70$
   - $5R + 11J \leq 61$
   - $9R + 14J \leq 37$
   - $-8R + 5J \geq 0$

4. Variable constraints:
   - $R$ must be an integer.
   - $J$ can be a fraction.

## 3: Convert the problem into Gurobi code.

To solve this problem using Gurobi, we will first import the necessary libraries, then define the model, variables, objective function, and constraints.

```python
import gurobi as gp

# Define the model
model = gp.Model("Optimization_Problem")

# Define the variables
R = model.addVar(name="Ringo_hours", vtype=gp.GRB.INTEGER)  # Integer hours for Ringo
J = model.addVar(name="John_hours")  # Continuous hours for John

# Define the objective function
model.setObjective(9 * R + 2 * J, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(6 * R + 12 * J >= 52, name="Productivity_rating_min")
model.addConstr(7 * R + 11 * J >= 52, name="Dollar_cost_min")
model.addConstr(5 * R + 11 * J >= 21, name="Likelihood_to_quit_min")
model.addConstr(9 * R + 14 * J >= 21, name="Paperwork_competence_min")

model.addConstr(6 * R + 12 * J <= 94, name="Productivity_rating_max")
model.addConstr(7 * R + 11 * J <= 70, name="Dollar_cost_max")
model.addConstr(5 * R + 11 * J <= 61, name="Likelihood_to_quit_max")
model.addConstr(9 * R + 14 * J <= 37, name="Paperwork_competence_max")

model.addConstr(-8 * R + 5 * J >= 0, name="Linear_constraint")

# Optimize the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Ringo's hours: {R.varValue}")
    print(f"John's hours: {J.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```