To tackle this optimization problem, we first need to establish a clear symbolic representation of the variables and constraints involved.

### Symbolic Representation:

Let's denote:
- $x_1$ as the hours worked by Ringo,
- $x_2$ as the hours worked by Jean.

The objective function is to minimize: $8x_1 + 4x_2$

Given the constraints:
1. Likelihood to quit index for Ringo is 4, and for Jean is 3.
2. Organization score for Ringo is 3, and for Jean is 1.
3. Paperwork competence rating for Ringo is 1, and for Jean is 3.
4. Work quality rating for Ringo is 3, and for Jean is 2.
5. Computer competence rating for Ringo is 5, and for Jean is 1.

And the combined constraints:
- Total likelihood to quit index $\geq 10$ and $\leq 27$
- Total organization score $\geq 9$ and $\leq 10$
- Total paperwork competence rating $\geq 16$ and $\leq 30$
- Total work quality rating $\geq 7$ and $\leq 26$
- Total computer competence rating $\geq 7$ and $\leq 19$
- $-9x_1 + 5x_2 \geq 0$

### Symbolic Representation in JSON Format:
```json
{
    'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by Jean')],
    'objective_function': '8*x1 + 4*x2',
    'constraints': [
        '4*x1 + 3*x2 >= 10', '4*x1 + 3*x2 <= 27',
        '3*x1 + 1*x2 >= 9', '3*x1 + 1*x2 <= 10',
        '1*x1 + 3*x2 >= 16', '1*x1 + 3*x2 <= 30',
        '3*x1 + 2*x2 >= 7', '3*x1 + 2*x2 <= 26',
        '5*x1 + 1*x2 >= 7', '5*x1 + 1*x2 <= 19',
        '-9*x1 + 5*x2 >= 0'
    ]
}
```

### Gurobi Code:
```python
from gurobipy import *

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

# Add variables to the model
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Ringo")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Jean")

# Set the objective function
m.setObjective(8*x1 + 4*x2, GRB.MINIMIZE)

# Add constraints to the model
m.addConstr(4*x1 + 3*x2 >= 10, "likelihood_to_quit_index_min")
m.addConstr(4*x1 + 3*x2 <= 27, "likelihood_to_quit_index_max")
m.addConstr(3*x1 + 1*x2 >= 9, "organization_score_min")
m.addConstr(3*x1 + 1*x2 <= 10, "organization_score_max")
m.addConstr(1*x1 + 3*x2 >= 16, "paperwork_competence_rating_min")
m.addConstr(1*x1 + 3*x2 <= 30, "paperwork_competence_rating_max")
m.addConstr(3*x1 + 2*x2 >= 7, "work_quality_rating_min")
m.addConstr(3*x1 + 2*x2 <= 26, "work_quality_rating_max")
m.addConstr(5*x1 + 1*x2 >= 7, "computer_competence_rating_min")
m.addConstr(5*x1 + 1*x2 <= 19, "computer_competence_rating_max")
m.addConstr(-9*x1 + 5*x2 >= 0, "additional_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Ringo: {x1.x}")
    print(f"Hours worked by Jean: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```