To solve this optimization problem, we'll use Gurobi, a powerful solver for linear and mixed-integer programming problems. The problem involves minimizing an objective function subject to various constraints related to hours worked by two individuals, Ringo and Jean, and their respective attributes.

Given the complexity of the problem with multiple constraints and variables, we will break down the solution into steps:

1. Define the decision variables.
2. Formulate the objective function.
3. Express the constraints mathematically.

### Decision Variables:
- Let \(x_0\) be the hours worked by Ringo.
- Let \(x_1\) be the hours worked by Jean, which must be an integer.

### Objective Function:
The objective is to minimize \(8x_0 + 4x_1\).

### Constraints:
Based on the provided information, we have several constraints. However, some constraints seem redundant (e.g., stating a minimum and then restating it as "at minimum" without additional information), so we'll focus on capturing the unique constraints:

1. **Likelihood to quit index**: \(4x_0 + 3x_1 \geq 10\) and \(4x_0 + 3x_1 \leq 27\).
2. **Organization score**: \(3x_0 + x_1 \geq 9\) and \(3x_0 + x_1 \leq 10\).
3. **Paperwork competence rating**: \(x_0 + 3x_1 \geq 16\) and \(x_0 + 3x_1 \leq 30\).
4. **Work quality rating**: \(3x_0 + 2x_1 \geq 7\) and \(3x_0 + 2x_1 \leq 26\).
5. **Computer competence rating**: \(5x_0 + x_1 \geq 7\) and \(5x_0 + x_1 \leq 19\).
6. **Additional constraint**: \(-9x_0 + 5x_1 \geq 0\).

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

```python
from gurobipy import *

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

# Define the decision variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Ringo")
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Jean")

# Objective function: Minimize 8*x0 + 4*x1
m.setObjective(8*x0 + 4*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(4*x0 + 3*x1 >= 10, "Likelihood_to_quit_index_min")
m.addConstr(4*x0 + 3*x1 <= 27, "Likelihood_to_quit_index_max")
m.addConstr(3*x0 + x1 >= 9, "Organization_score_min")
m.addConstr(3*x0 + x1 <= 10, "Organization_score_max")
m.addConstr(x0 + 3*x1 >= 16, "Paperwork_competence_rating_min")
m.addConstr(x0 + 3*x1 <= 30, "Paperwork_competence_rating_max")
m.addConstr(3*x0 + 2*x1 >= 7, "Work_quality_rating_min")
m.addConstr(3*x0 + 2*x1 <= 26, "Work_quality_rating_max")
m.addConstr(5*x0 + x1 >= 7, "Computer_competence_rating_min")
m.addConstr(5*x0 + x1 <= 19, "Computer_competence_rating_max")
m.addConstr(-9*x0 + 5*x1 >= 0, "Additional_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Ringo: {x0.x}")
    print(f"Hours worked by Jean: {x1.x}")
else:
    print("No optimal solution found.")
```