## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Ringo' and 'hours worked by Jean'. Let's denote 'hours worked by Ringo' as $x_1$ and 'hours worked by Jean' as $x_2$. The objective function to minimize is $8x_1 + 4x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $4x_1 \geq 4$ (Ringo's likelihood to quit index is 4)
- $3x_1 \geq 3$ (Ringo's organization score is 3)
- $1x_1 \geq 1$ (Ringo's paperwork competence rating is 1)
- $3x_1 \geq 3$ (Ringo's work quality rating is 3)
- $5x_1 \geq 5$ (Ringo's computer competence rating is 5)
- $3x_2 \geq 3$ (Jean's likelihood to quit index is 3)
- $1x_2 \geq 1$ (Jean's organization score is 1)
- $3x_2 \geq 3$ (Jean's paperwork competence rating is 3)
- $2x_2 \geq 2$ (Jean's work quality rating is 2)
- $1x_2 \geq 1$ (Jean's computer competence rating is 1)
- $4x_1 + 3x_2 \geq 10$ (total combined likelihood to quit index)
- $3x_1 + 1x_2 \geq 9$ (total combined organization score)
- $1x_1 + 3x_2 \geq 16$ (total combined paperwork competence rating)
- $3x_1 + 2x_2 \geq 7$ (total combined work quality rating)
- $5x_1 + 1x_2 \geq 7$ (total combined computer competence rating)
- $-9x_1 + 5x_2 \geq 0$ (specific linear combination of hours worked)
- $4x_1 + 3x_2 \leq 27$ (total combined likelihood to quit index upper bound)
- $3x_1 + 1x_2 \leq 10$ (total combined organization score upper bound)
- $1x_1 + 3x_2 \leq 30$ (total combined paperwork competence rating upper bound)
- $3x_1 + 2x_2 \leq 26$ (total combined work quality rating upper bound)
- $5x_1 + 1x_2 \leq 19$ (total combined computer competence rating upper bound)

## 3: Consider variable bounds and types
- $x_1$ can be a non-integer.
- $x_2$ must be an integer.

## 4: Formulate the problem in Gurobi
We will use Gurobi's Python API to formulate and solve this problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define variables
x1 = m.addVar(name="hours_worked_by_Ringo", lb=0)  # No upper bound given
x2 = m.addVar(name="hours_worked_by_Jean", lb=0, type=gp.GRB.INTEGER)

# Objective function
m.setObjective(8 * x1 + 4 * x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(4 * x1 >= 4)
m.addConstr(3 * x1 >= 3)
m.addConstr(x1 >= 1)
m.addConstr(3 * x1 >= 3)
m.addConstr(5 * x1 >= 5)

m.addConstr(3 * x2 >= 3)
m.addConstr(x2 >= 1)
m.addConstr(3 * x2 >= 3)
m.addConstr(2 * x2 >= 2)
m.addConstr(x2 >= 1)

m.addConstr(4 * x1 + 3 * x2 >= 10)
m.addConstr(3 * x1 + x2 >= 9)
m.addConstr(x1 + 3 * x2 >= 16)
m.addConstr(3 * x1 + 2 * x2 >= 7)
m.addConstr(5 * x1 + x2 >= 7)

m.addConstr(-9 * x1 + 5 * x2 >= 0)

m.addConstr(4 * x1 + 3 * x2 <= 27)
m.addConstr(3 * x1 + x2 <= 10)
m.addConstr(x1 + 3 * x2 <= 30)
m.addConstr(3 * x1 + 2 * x2 <= 26)
m.addConstr(5 * x1 + x2 <= 19)

# Solve the model
m.optimize()

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

## 5: Symbolic Representation
The symbolic representation of the problem is as follows:

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